The tough-talking billionaire's meeting with Pena Nieto was expected to begin around 1900 GMT at Los Pinos, the presidential residence.
Local media said Trump would fly by helicopter to Los Pinos for the meeting and would later make a statement to the press.
Trump stunned the political establishment when he announced late Tuesday that he was making the surprise trip south of the border for a face-to-face encounter with the leader of a neighbor and close US ally who is also one of his sharpest critics.
The closed-door meeting takes place just hours before Trump delivers a highly-anticipated speech on immigration, and as debate about his hardline policies -- including his call for building a border wall and having Mexico pay for it -- reaches fever pitch.
Pena Nieto has categorically rejected the idea of his country paying for a wall, and has gone so far as to compare the Republican candidate to Hitler and Mussolini.
Trump's visit holds potential political peril, as many in Mexico loathe him for his toxic rhetoric.
"Trump not welcome in Mexico, not by me nor the 130 million Mexicans," the country's former president Vicente Fox, who dropped an "f-bomb" on television in February when describing Trump's border wall, said on Twitter.
He blasted the visit as a "political stunt" aimed at boosting the tanking poll numbers of Pena Nieto, who was taking an "enormous political risk" by hosting Trump.
"If he's gone soft on Trump, it will hurt him greatly," Fox told CNN.
Trump's campaign director Kellyanne Conway said he and Pena Nieto would address immigration, along with drug smuggling and trade.
The invitation by Pena Nieto comes with just 69 days to go before the US presidential election.
With Trump trailing Democrat Hillary Clinton in most polls, the trip could allow him to seize control of the campaign narrative at a crucial time and capitalize on dramatic optics that put him on the stage with a global leader.
Pena Nieto, who was elected in 2012, also invited Clinton, but the former secretary of state's campaign has announced no plans for a visit.
Clinton took the more traditional approach on the campaign trail Wednesday, addressing an American Legion meeting in Ohio where she upbraided Trump for his Mexican "photo op" and signalled it was no way to build leadership credibility.
"It certainly takes more than trying to make up for a year of insults and insinuations by dropping in our on neighbors for a few hours and then flying home again. That is not how it works," Clinton said.
Trump has routinely assailed Mexican immigrants who illegally cross the border into the United States. Hardline immigration policies are a key plank of his campaign.
Trump used some of the most incendiary language of his campaign when launching his White House bid last year, describing Mexicans as drug dealers, "rapists" and criminals.
He is scheduled to deliver what is billed as a crucial speech Wednesday evening in Phoenix, Arizona, seen as an opportunity to clarify his policy.
But Trump has vacillated between reaching out to minorities and returning to the anti-immigration rhetoric that is admired by his most ardent supporters, mainly white working-class males.
"Donald Trump is... not your standard issue politician, but really a business leader that knows you first got to sit down with people," his running mate Mike Pence told CNN, adding that the Trump-Pena Nieto meeting would be the "beginning of a conversation."
"You've got to look them in the eye. You've got to tell them where you stand."
Trump has vowed to renegotiate the North American Free Trade Agreement that he blames for the relocation of US factories to Mexico and the loss of millions of US manufacturing jobs.
Last year, Trump pledged to create a deportation force dedicated to rounding up those illegally in the country.
In recent weeks, he has expressed willingness to soften his hardline stance to a "fair and humane" policy ahead of November's election.
Pena Nieto has insisted he is committed to defending Mexican interests and to work with the future US president, whoever it will be.
But Trump's arrival has infuriated observers, including Mexican historian Enrique Krauze, who described the invitation as a "historic mistake."
"This is a dubious way to defend the interests of Mexico," the president of the Chamber of Deputies, the lower house of Congress, Jesus Zambrano told AFP.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)