The left-wing anti-establishment candidate, Andrés Manuel López Obrador, will make tackling corruption his top priority after winning Mexico's presidential election on Sunday.
Official projections give him more than 53% of the vote but it is unclear whether his party will secure an outright majority in parliament.
US President Donald Trump has said he looks forward to working with him.
Trade and migration disputes have strained US relations with Mexico.
Mr López Obrador, 64, has said he wants to make his country more economically independent of the US while also persuading Mr Trump to help develop the region in order to contain illegal migration.
He inflicted a crushing defeat on the candidates of the two big established parties, Ricardo Anaya of the National Action Party (PAN) and José Antonio Meade of the Institutional Revolutionary Party (PRI), with independent Jaime Rodríguez Calderón trailing in fourth place.
However, it is still unclear whether the winning candidate's own party, the National Regeneration Movement (Morena), and its allies can secure an overall majority in Mexico's Congress and Senate.
Under Mexico's constitution, Sunday's winner will not actually be sworn in as president until 1 December.
A night they won't forget
By Will Grant, BBC News, Mexico City
It was a night his supporters will remember for the rest of their lives. They descended in their thousands to Mexico City's main square, the Zocalo, to celebrate that after 12 years of frustration, finally their man will be president.
Perhaps the wait was worth it. Given the exhaustion with the widespread corruption, violence and impunity in Mexico, not only did Mr López Obrador win by a huge margin, expected to be more than 30%, his new coalition, Morena, destroyed the governing conservative PRI party at a local and state level too.
So much so, in fact, that the PRI will now be one of the smaller parties in Congress. Congratulations were sent by international leaders from Nicolás Maduro in Venezuela to President Trump.
Certainly they will have a lot to talk about, with everything from the border wall to the North American Free Trade Agreement a potential source of friction. Still, for now, those jubilant supporters will just be savouring the victory.
What did he say about corruption?
"We are absolutely convinced that this evil is the main cause of social and economic inequality, and also that corruption is to blame for the violence in our country," Mr López Obrador said in a speech to supporters.
No-one involved in corruption will be spared, he said, not even "brothers-in-arms".
He repeated his campaign pledge to review energy contracts for signs of corruption.
Mexico is perceived as one of the most corrupt countries in the world, according to Transparency International, which ranked it 135 out of 180 states last year, with 180 being the most corrupt.
Corruption scandals damaged the standing of the PRI during the campaign.
Earl Wayne, US ambassador to Mexico until 2015, voiced some scepticism as to whether Mr Lopez Obrador would be successful in his efforts.
"He's been quite clear in attacking it and it is one of the real weaknesses of Mexico," Mr Wayne told the BBC.
"But actually transforming that rhetoric into cases against the corrupt that are actually successful will be a major task given the weakness in Mexico's law enforcement and judicial system."
What are his other main policies?
According to Reuters news agency, Mr Lopez Obrador said he would be respectful of the current Mexican government team reviewing the North American Free Trade Agreement (Nafta).
The Trump administration wants to renegotiate the 1994 agreement with Mexico and Canada, which created one of the world's largest free trade zones.
During the campaign Mr López Obrador often used confrontational language when referring to Mr Trump but struck a more conciliatory note in his victory speech, saying he would seek "friendly relations".
On combating Mexico's record levels of violence, much of it related to drug cartels, Mr López Obrador said he would have daily meetings with his security cabinet.
He also tried to reassure the business sector, saying there would be no nationalisation, private business would be respected and taxes would not be raised.
On social policies, he promised to double pensions for the elderly as a first step to reducing the country's disparate income levels.
Some opponents have expressed fears that his leftist and populist policies could damage the already sluggish economy.
Who is López Obrador?
- Born to a family of shopkeepers on 13 November 1953 in the rural community of Tepetitán, in southern Tabasco state
- Known popularly as Amlo, which is an acronym using the full initials of his name
- Elected Mexico City mayor in 2000
- After losing the presidential elections in 2006 and 2012, he ran again this time under a three-party coalition led by the leftist National Regeneration Movement party (Morena) he founded in 2014
- The self-styled anti-establishment figure has now ended the dominance of the PRI and PAN parties he called the "mafia of power"