He wants to boost economic growth and cut drug-related violence, but analysts say it is not clear how he will do so.
Some 60,000 people have been killed in drug-related violence during the rule of his predecessor, Felipe Calderon.
As Enrique Pena Nieto’s motorcade approached Congress, petrol bomb-wielding protesters clashed with riot police who fired tear gas outside the building.
One protester was gravely injured after being hit with a tear gas canister.
The demonstrators are angry at what they say was vote-buying by the president’s campaign.
They were also protesting more generally against the return to power of Enrique Pena Nieto’s Institutional Revolutionary Party (PRI) after a 12-year absence.
Amid a cacophonic trumpet fanfare, outgoing President Felipe Calderon handed a sash with the colors of the Mexican flag to Enrique Pena Nieto, who was expected to address the nation from the presidential palace later on Saturday.
All week in Mexico City, a ring of steel had been in place around the Congress building ahead of the ceremonial presidential inauguration.
It had created massive traffic jams in the already congested city as authorities tried to prevent protesters from gaining access to parliament.
Earlier, the new president, who is 46, named a 20-member cabinet.
His foreign minister will be Jose Antonio Meade, who was treasury minister in Felipe Calderon’s outgoing government.
Enrique Pena Nieto spent his final days as president-elect in talks with leaders in the US and Canada, Mexico’s partners in the regional trade organisation, Nafta.
The PRI governed without interruption for 71 years until 2000, and its opponents often accused it of being authoritarian and corrupt, and of having links to the drug cartels.
But during his election campaign Enrique Pena Nieto was adamant the party had evolved.
“I can say categorically that in my government, there won’t be any form of pact or agreement with organized crime,” he said.
“It’s not the path nor the route to greater security for the Mexican people.”
Earlier this month, he denied the PRI’s return to power would be a return to the past.
“It is not, because this is a different country,” he said.
Enrique Pena Nieto has indicated he will focus on tackling extortion, kidnapping and murder, and he has drafted in support from Colombia’s former top policeman.
The outgoing president is due to take up a position at Harvard University and maintains he has made Mexico safer.
But for many Mexicans, Felipe Calderon’s legacy as president is of an estimated 10,000 drug-related killings a year for the past six years.
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