During a half-hour telephone conversation, Mr Trump said the two leaders discussed topics including border security, trade and the North American Free Trade Agreement, adding that "I think the relationship will be a very good one".
Queuing under the hot sun at Tijuana polling booths, many Mexican voters who had crossed the border from California told Reuters that they trusted Lopez Obrador most to protect the roughly 12 million Mexicans living in the United States. Many undocumented immigrants and asylum seekers from Central America pass through Mexico before trying to enter the United States. These are all factors that point to a stalemate, said Moshe Lander, an economist at Concordia University.
"We are not going to fight".
"Congratulations to Andres Manuel Lopez Obrador on becoming the next President of Mexico".
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. "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.
"I'm looking forward to conciliation to seek an organized transition for everyone", Lopez Obrador told reporters, who pushed and shoved in a bid to speak with him.
She said a Lopez Obrador presidency is a good way to kick the ruling Institutional Revolutionary Party, or PRI, out of power. He said contracts obtained under energy reforms passed under President Enrique Pena Nieto will be scrutinized for any corruption or illegality, but otherwise contracts will be honored.
Lopez Obrador vows to improve lives for Mexicans and the country's global reputation by ending corruption, applying the law and reducing the wealth gap. It is also the first time Mexicans living overseas can vote for down ballot races like senators.
The peso was trading at 20.11 per dollar on Monday morning.
Exit polls Sunday evening showed Lopez Obrador had won by a large margin, and his rivals both conceded shortly after polls closed.
"This man is the only one who can make Trump end his persecution and racism against Mexicans", said Luis Evans, 58, who drove from Los Angeles to a voting booth about a mile from the border.
Refusing to live in Mexico City's opulent 19th century presidential residence, Los Pinos (the Pines). He has also proposed a diversified approach towards commerce, recognising the risk of betting the country's economic fortunes on the US.
The coalition was set to win governorships in the states of Veracruz, Morelos, Chiapas and Tabasco, as well as Mexico City, where a woman was elected for the first time ever, the Jewish scientist and environmentalist Claudia Sheinbaum.
Voters will expect him to put into concrete action his anti-corruption agenda, reign in rising killings and cartel violence that have stubbornly resisted the efforts of his two predecessors, and revive a sluggish economy that grew just 2.1 per cent a year ago. He has also promised to increase spending on social programs while keeping government spending under control.