Labour's Sir Lindsay Hoyle has been re-elected as Commons Speaker, as MPs return to Parliament after the election.
Sir Lindsay pledged his office would be "open to all," after he was returned unopposed into the role he first took up last month.
The process of "swearing in" MPs has begun, and the government will outline its legislative plans on Thursday.
They will be asked to vote on the PM's Brexit deal bill on Friday.
Speaking in the Commons for the first time since gaining an 80-seat majority in last week's poll, Boris Johnson pledged to "find common ground" with other parties.
The prime minister pledged to end "three and a half years of wrangling and division" in Parliament, and repeated his campaign pledge to "get Brexit done".
He vowed that the "people's Parliament" would be "vastly more democratic" and a "vast improvement on its predecessor".
"This Parliament is not going to waste the time of the nation in deadlock, and division and delay," he added.
Mr Johnson was welcomed with a huge cheer by his backbenchers as he arrived in the Commons, contrasting with a much more muted greeting for his Labour counterpart Jeremy Corbyn.
Mr Corbyn congratulated the prime minister on his election victory, and said he would be "judged" on the "many, many promises" he made during the campaign.
"Our job in the Labour party will be to hold this government to account, and stand up for the communities that we represent," he added.
Mr Corbyn will step down in the new year after the party slumped to its worst election performance since 1935.
A number of possible contenders are in the frame for the contests to replace them that will take place next year.
Mr Corbyn is expected to address a closed-door meeting of Labour MPs later on Tuesday for the first time since the election.
Meanwhile, the government has said a new clause will be added to its Brexit bill to rule out any extension to the post-Brexit transition period.
The amended Withdrawal Agreement Bill would seek to prevent ministers from prolonging the 11-month period, due to conclude in December 2020.
Ministers say they will use this time to reach a trade agreement with the EU, but critics say this will not be possible.
However with its large majority, the government could in theory overturn the Act if ever it did wish to extend the transition.
What will happen this week?
Tuesday and Wednesday
The process of swearing in MPs continues. They are required to take an oath of allegiance to the Crown, or, if they object to this, a solemn affirmation. Those who speak or vote without having done so are deprived of their seat "as if they were dead" under the Parliamentary Oaths Act of 1866.
Two to three days are usually set aside for this process.
The state opening of Parliament. The Queen's Speech is the centrepiece of this, when she will read a speech written by ministers setting out the government's programme of legislation for the parliamentary session. A couple of hours after the speech is delivered, MPs will begin debating its contents - a process which usually takes days.
Depending on how rapidly Boris Johnson wants to move, the debate on the Queen's Speech could continue into Friday.
The government will introduce the Withdrawal Agreement Bill to Parliament.
MPs in the previous Parliament backed Mr Johnson's bill at its first stage but rejected his plan to fast-track the legislation through Parliament in three days in order to leave the EU by the then Brexit deadline of 31 October.
After the debate on the Queen's Speech is concluded, MPs will vote on whether to approve it. Not since 1924 has a government's Queen Speech been defeated.