With almost three-quarters of the ballots counted, Lopez Obrador had about 53 per cent of the vote - the most for any presidential candidate since 1982, a time when the Institutional Revolutionary Party was in its 71-year domination of Mexican politics and ruling party victories were a given.
Polls had tipped a wide victory for Lopez Obrador, who many investors are expecting will govern from the center.
Surveys conducted by Consulta Mitofsky and Televisa forecast gubernatorial wins for allies of the Morena party in Chiapas, Morelos, Tabasco and Veracruz, and for head of government in Mexico City.
Shortly afterwards, Lopez Obrador gave his account of the call in a Twitter post, saying he had proposed a comprehensive deal to create jobs, lower immigration and improve security. "I confess that I have a legitimate ambition: I want to go down in history as a good president of Mexico", he said after announcing his landslide victory. He said he will seek a relationship of "friendship and respect" with the United States.
Haq said the U.N. chief "expresses the readiness of the United Nations to work with the new administration continuing a longstanding tradition of excellent cooperation between Mexico and the United Nations".
However, opponents of Mr Lopez Obrador say he could turn Mexico into another Venezuela - where the authoritarian left-wing governments of Hugo Chavez and his successor Nicolas Maduro wrecked the economy and fostered corruption and political violence. He is member of the National Regeneration Movement (MORENA) party.
"The revolution of consciences has triumphed", the victor told tens of thousands of jubilant supporters who had gathered on Mexico City's central Zocalo Square.
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Local news reports said a neighbour made the grisly discovery after checking on the family after they failed to open their shop. Indian TV channels broadcast interviews with neighbours who said the family did not have any discord among themselves.
Dayra Valdes is a Mexican-born migrant who calls Anchorage home. "I am concerned that some candidates are making proposals that are impossible, because they're very expensive to carry out", said Juan Carlos Limas, 26, who lined up at another Mexico City precinct to vote for Ricardo Anaya, who is running second in polls for a right-left coalition.
Lopez Obrador has said he will fund increased social spending on pensions for the elderly and scholarships for youths by eliminating waste and fighting corruption.
Trump has been highly critical of Mexico's control of its border.
Donald Trump also congratulated Lopez Obrador on his electoral win, however, the USA president also said in an interview this weekend he intends to hold off on signing a new NAFTA deal until after America's fall midterm elections.
Officials estimated voter turnout at 63 percent among the 89 million people who were eligible to vote in Mexico's biggest-ever elections. In both of Lopez Obrador's previous two presidential losses he alleged fraud.
Prime Minister Justin Trudeau meets with outgoing Mexican President Enrique Pena Nieto in Lima, Peru on Friday, April 13, 2018.
"I see that the results [of the voting] are favorable for Lopez Obrador". But Duncan also said that many people are unsure of how Lopez Obrador will be able to provide what he has promised.
"We would not want this organism to be any way partisan", he said.