Britain's Labour Party leader, Jeremy Corbyn, was among the first to offer Mr Lopez Obrador congratulations, who on Sunday night won in the largest landslide in his country's recent history.
Lopez Obrador, who will take office on December 1, won more than 53 per cent of votes in Sunday's election, preliminary results showed, more than double the votes of his nearest rival.
Mexico recorded about 29,000 killings past year, the highest annual number since modern records started being kept two decades ago.
Mexicans also voted for members of both houses of Congress and nine governors.
Pena Nieto, whose approval ratings stood at only about 20 per cent, was limited by the constitution to a single term.
He has called for a respectful relationship between the U.S. and Mexico, but criticized U.S. President Donald Trump's plan for a border wall. He even wrote a book titled Oye Trump (Listen up, Trump) in which he criticised Nieto for not representing Mexico with dignity and condemned the border wall and Mexican "passivity" in its relations with the US.
Trump has been highly critical of Mexico's control of its border.
He also once referred to Mr Trump as "erratic" and "arrogant" at a rally in Mexico City, NPR reported and also criticised Mr Trump's campaign promise to build a wall and said: "we won't allow his wall or mistreatment of our fellow migrants in the U.S.".
On Monday, an advisor to Lopez Obrador told Reuters the election win would jumpstart talks between Mexico, the United States and Canada to renegotiate the North American Free Trade Agreement, known as NAFTA.
"Trump tweeted Sunday that "I look very much forward to working with him".
Of greatest importance here, though, may be the same thing that moved Mexicans to overwhelmingly choose the left-wing populist leader (and two-time failed presidential candidate) over his more staid rivals: Mexico's long-standing inability to deal with corruption and gang violence. "But we will give preference to the most humble and forgotten", he said after being confirmed the victor by the current president Enrique Peña Nieto of the PRI party that lost power for the first time in 2000 and regained it in 2012. "I will not disappoint you and I will not betray my people", he said.
Trump has been antagonistic to Mexico over trade and immigration.
Exit polls gave its candidate Claudia Sheinbaum as the new Mexico City mayor, while the party was also expected to win governorships in the states of Chiapas, Tabasco and Morelos.
Retired Susana Zuniga beamed as she said the country was experiencing a moment similar to the Mexican Revolution a century ago.
"The people are fed up", Zuniga said.
"We won't do the dirty work of any foreign government", AMLO said, referring to detentions of Central American migrants trying to reach the United States border.
Lopez Obrador also said he would form joint teams with Pena Nieto's administration to analyse the $13 billion Mexico City airport project, which he has repeatedly threatened to scrap, and see what is the best course of action. Driver is the author of "More or Less Dead: Feminicide, Haunting, and the Ethics of Representation in Mexico". News reports say that more than 100 politicians were killed in the campaign leading up to Sunday's vote.
In this photo released by Mexico's presidential press office, Lopez Obrador, right, is escorted by current President Enrique Pena Nieto through the National Palace.
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