Opposition leader Zephirin Diabre has been speaking to Newshour on the BBC World Service.
He said he expected there would be "a round table with all the political forces, civil society, [and] the army, and then we can agree on the format of the transition".
It could be a year before elections are held, he added. "Because you need to revive the constitution, maybe draw up a new constitution. That would take at least 12 months."
A crowd gathered in front of the army headquarters earlier on Friday, demanding the army takeover.Copyright: AFP
The BBC's Yacouba Ouedraogo in Ouagadougou confirms what many have sensed about there being divisions within the army:
There appears to be a split in the army over who should lead the transition. Col Yacouba Isaac Zida has said that he will lead the transition, not Gen Traore - who is not popular with the people.
The civil society group Balais Citoyen, which has been instrumental in organising the demonstrations, backs him as did the crowds he addressed.
But little is known about Col Zida except that at one stage he was deputy commander of the presidential RSP guard.
Video of the moment General Honore Traore announced his takeover of power on national television.Copyright: Reuters
Another man likely to wield major influence in the next few months in Burkina Faso is opposition leader Zephirin Diabre, who has just held a press conference in Ouagadougou.Copyright: AFP
Here is Colonel Isaac Zida (centre), who has been touted as a possible rival to General Traore, the current interim leader of Burkina Faso.Copyright: AFP
Benedict Owusu-Yankyera in the southern city of Bobo Dioulaso emails: Celebrations are taking place in Bobo Dioulaso with hooting of horns in the streets. They seem comfortable with the results of the demonstrations. The people had gathered earlier in the morning but later upon knowing of the resignation they dispersed.
BBC diplomatic correspondent
What happens next in Burkina Faso matters profoundly to the United States and its allies as well. Washington has a huge embassy in Burkina Faso, an important intelligence and military planning centre in a country which is one of the counters to Islamist forces, particularly in neighbouring Mali.
BBC diplomatic correspondent
What's happening in Burkina Faso has implications for several other leaders in the region and across Africa - those who have clung to power despite pressure, particularly from the young, who have been denied jobs and hope by a combination of corruption, cronyism and disastrous economic mismanagement. Now the people will watch nervously to see if the head of the armed forces who has taken control honours the promise of free elections within 90 days.
President Blaise Compaore's resignation came after Thursday's protests in the capital Ouagadougou turned violent. Our reporter Laeila Adjovi was at the scene, and compiled a picture gallery.Copyright: BBC
Christabelle Uffey, CNN International Assignment Editor
tweets: As he resigned from presidency Friday, Blaise Compaore, appealed for "free elections to be held in Burkina Faso within 90 days at the most".
Senam Beheton tweets: Transition structure still very fluid. As expected, many don't want Gnl Honore Traore to lead transition. #lwili
Joe Bavier, Reuters correspondent based in Abidjan
tweets: Very unclear what is going on between Traore (head of army) and Zida (I'm told commander in prez security detachment). #lwili
CBC News Alerts
tweets: Canadian embassy in #BurkinaFaso remains closed as 'safety precaution.' Army in control of country after protests, resignation of president.
General Honore Traore (centre) announced his takeover of power at the army headquarters earlier today,Copyright: Reuters
A pattern is emerging among many of those on the streets of Ouagadougou and people who have been in touch with us, who view the new leader General Traore with suspicion.
"We do not want General Traore in power. We need someone credible. Traore is Blaise Compaore's henchman," opposition activist Monou Tapsoaba tells AFP news agency.
This Reuters photo shows looting allegedly taking place at the residence of Francois Compaore, the younger brother of deposed president Blaise Compaore.Copyright: Reuters
A reader in Ouagadougou emails: Here lots of cars peeping horns and crowds are shouting in my neighbourhood.
I don't live too far from the Place de la Nation. We're still hearing reports of looting though which is worrying.
BBC News, Kinshasa
The news from Burkina Faso is of significance in the Democratic Republic of Congo, where some members of the the ruling party have called for a constitutional change to allow President Joseph Kabila to run for a third term.
One man in the capital, Kinshasa, told the BBC: "I want to use this opportunity to tell our politicians that what is happening there could also happen here in the DRC, it is possible. If we see that the people in power want to change things in order to stay in power, we will not accept it."
Joe Penney, Reuters photojournalist
tells the BBC: "I was greeted with lots of joy in the streets of Ouagadougou; people riding around on their motorcycles, chanting and singing and dancing, just general scenes of joy throughout the city. But one thing is that they don't really like Honore Traore, the new president. So, they were celebrating their victory over Blaise Compaore but not the new president."
BBC News, Ouagadougou
says there might be a new contender on the scene, in the form of army Colonel Isaac Zida, who has reportedly told protesters in Place de la Nation that the constitution has now been suspended.
Steve Amodio in Ouagadougou emails: Everyone is celebrating, but they were waiting more for the announcement of who will take power. I think there are a lot of mixed feelings.
We are all excited for the possibilities of the future. The old mayor Simon Compaoré came out and asked people to come out and clean up the city tomorrow. But the problem is Blaise is running to the border, there is no real confirmation as to the location of Francois Compaoré [Blaise Compaore's brother] and the looters are still taking advantage of the situation. We need the police and military to secure the city before too much damage is done. And it not the opposition. They have been well organised. It's the people trying to take advantage of the situation.
Two women pose in front of an armoured vehicle in the capital Ouagadougou.Copyright: AFP
A demonstrator at Place de la Nation in Ouagadougou tells the BBC that protesters do not want General Traore to lead the country and want former Defence Minister General Kouame Lougue instead.
"This hasn't been a coup d'etat. That was a popular uprising. We rose up, we fought and we won, and now we are saying we want this man to lead. So, why do they want to force us to accept a man who doesn't do it for us?"
reports: The hashtag #lwili is being used in Burkina Faso to spread news about the protests. The word lwili, which means bird in the local Moore language, was chosen at a meeting of Twitter users in Ouagadougou.
Reuters photographer Joe Penney tweets: "People finally got to loot and burn François Compaoré's house just now. Yesterday was scene of army firing on protesters #Burkina"
BBC West Africa correspondent
An armed convoy believed to be that of the now-outgoing president was seen leaving the capital Ouagadougou heading towards the border with Ghana.
BBC West Africa correspondent
As people celebrate Mr Compaore's resignation, many are also worried that General Traore, close to the outgoing president, may try to steal their popular action. General Traore is meant the lead the country towards an election within the next three months. But he's now got all the cards in hands.
Huge crowds have gathered at the Place de la Nation in Ouagadougou to welcome the news of President Compaore's resignation.Copyright: Reuters
President Compaore has "left for the south" of Burkina Faso, but is "still in the country", a French diplomatic source, who did not want to be named, tells AFP news agency.
What sort of legacy will Mr Compaore leave behind? BBC News looks back at his 27 years in power.Copyright: AFP
BBC News, Ouagadougou
says that many protesters in the capital are unhappy with the fact that army chief General Honore Traore is taking charge. They would much prefer former Defence Minister General Kouame Lougue, who left the government in 2003 following a disagreement with the president.
Anti-government protesters are celebrating in the capital following President Compaore's resignation.Copyright: AFP
One protester, who wanted to be known as Sam, told the BBC: "Blaise Compaore has gone away, he's running away and we are happy. The words are not coming so easy because I'm very happy, my children are going to know another president."
"People are still out on the streets in large numbers, and they're looting houses and shops - you can see motorcycles driving around with bags of rice, with furniture and mattresses that they got from some houses," Joost Laane, an expat living in Ouagadougou, told the BBC's Focus on Africa programme.
Burkina Faso's main opposition leader, Zephirin Diabre, tells the BBC's Focus on Africa radio programme: "We are all relieved by what is happening - and this is our demand for so long so we are very happy - and we need to work on the transition to take care of our country"
Gen Traore added: "I undertake a solemn engagement to proceed without delay with consultations with all parties in the country so as to start the process of returning to the constitutional order as soon as possible."
Armed forces chief General Honore Traore told a news conference: "Considering the urgency of saving the nation, I have decided that I will assume from this day the responsibility of the head of state."Copyright: AFP
Here's the full text of President Compaore's resignation statement, via BBC Monitoring:
"People of Burkina Faso, in view of the strongly weakened social-political situation that has been characterised by a persistent breakdown in public order; looting of public and private property; the threat of a split in the national army; and for the need to preserve the democratic gains, as well as social peace in our country, I have decided to invoke Article 43 of the constitution. I have declared a power vacuum to allow for the immediate establishment of a transitional [authority] that will result in free elections within 90 days at most.
"I appeal to the entire citizenry to remain calm, I urge political actors and the civil society to assume their responsibilities and stop the unrest that will only delay our march to development. For my part, I believe I have accomplished my task, and my only concern now is the greater good of the nation.
God bless Burkina Faso
(Signed) Blaise Compaore, President of Faso."
Ouborr Kutando in Ouagadougou emails: I am in Burkina Faso for a conference at the defunct Azalai Hotel.
A couple of us were in my room watching the demonstrators live. Gradually they trooped in the hotel and the looting begun. The hotel was stripped of everything from tea cups to air conditioners.
As the looting continued, we could hear them break room to room and when they got to my room, they pounded the door and met four of us frightened and waiting. Because they had not expected to see us, they panicked and asked us for money.
As I became a sitting duck in my room, all I could say was that, this presents great lessons for political sociology in African politics. Most of the looters were the youth who had spent all their life under Blaise.
There are scenes of jubilation in parts of Ouagadougou following the resignation of President Compaore, with residents beeping their car horns and chanting.Copyright: AFP
Yet over time Mr Compaore oversaw a startling transformation of his image, internationally at least. This inflammatory figure became a man relied upon to put out fires around the region. Over the years, he won a series of elections, though the opposition always complained that the odds were stacked dramatically in the president's favour.
"Controversy would be a perpetual feature of Blaise Compaore's time in power. The president was accused of stoking rebellions around West Africa. His name still provokes strong feelings in Sierra Leone and elsewhere."
reports : "I've been on the phone to a source in Ouagadougou. The President has stepped down and he has not stepped down to stay around, he has stepped down and he is on the move. And according to that source he might have crossed the border with Ghana. And he was heading towards Po which is a city somewhere near the border with Ghana."
Former colonial power France welcomes the resignation of President Compaore, reiterating its "support for the constitution and thus for early, democratic elections".
During protests this week, many in the crowd have been carrying posters of Thomas Sankara, the late president of Burkina Faso. Blaise Compaore took over power after Mr Sankara was killed in mysterious circumstances by a group of soldiers in 1987. Sometimes known as "Africa's Che Guevara", the BBC's Alex Duval Smith has looked at Sankara's enduring appealCopyright: AFP
The European Union has weighed in on the crisis in Burkina Faso, calling on people there to have the final say in who governs the West African country, AFP reports. It has also offered its help with organising elections.
Armed forces chief General Honore Traore has announced that he is taking charge, following President Blaise Compaore's resignation.
The Twitter account of Blaise Compaore has been posting excerpts from his statement, including calls for elections to be held within 90 days and an appeal for all citizens to remain calm.
tweets: You spend 27 years struggling to maintain your power base.. It takes just a day to send u packing.. We cant make these stuff up #BurkinaFaso
tweets: At press conference just now chief of defense staff honoré traoré announced resignation of blaise himself as president #burkina #lwili
Army chief General Honore Traore is to take over as head of state, Reuters reports.
Opposition parties had earlier urged protesters to return to the streets of Ouagadougou, a day after they ransacked parliament and set it alight.Copyright: Reuters
While Blaise Compaore's whereabouts remain unknown, Reuters reports that a heavily armed convoy believed to be carrying the ex-president was seen travelling near Burkina Faso's border with Ghana, in the southern town of Po.
An army officer from the presidential guard earlier announced Mr Compaore's departure to thousands of protesters in the central Place de la Nation. They reportedly responded with cheers.
Blaise Compaore had been in power since 1987, after his predecessor, Thomas Sankara, was killed in mysterious circumstances by a group of soldiers.Copyright: Reuters
In a presidential statement broadcast by local media, Mr Compaore declared a "power vacuum" in the country and called for "free and transparent" elections within 90 days.
Welcome to the BBC's live updates on the unravelling situation in Burkina Faso, where President Blaise Compaore has just announced his resignation in response to violent protests against his attempts to extend his 27-year-rule.