The vote – which was a show of hands in the packed Zocalo square – was the latest development in Mexico’s months-long electoral dispute.
The massive meeting took place just hours after Vicente Fox, the outgoing conservative president, celebrated independence day with a massive military parade in the square.
Lopez Obrador is to be sworn into his new post as “legitimate president” on November 20.
The vote was greeted by applause.
The parallel government plans to spend the next six years trying to keep Felipe Calderon, the president-elect, from governing.
Tens of thousands of left-wing supporters celebrated the traditional independence “grito”, or cry, in Mexico City’s Zocalo square on Friday night after forcing Vicente Fox, the outgoing president, to lead a separate ceremony outside the capital.
But the supporters removed squatter camps from the city centre, which it had blocked for nearly seven weeks in protest at what it says was fraud in the July 2 elections, to allow the military parade to go ahead on Saturday.
Fox and Calderon, a member of Fox’s conservative National Action Party, reviewed the parade as about 200 supporters of Lopez Obrador waved posters that read “Fox, traitor to democracy”.
But just minutes after the parade left the Zocalo, leftists moved back in, carrying the large yellow flags of the Democratic Revolution Party and preparing for the massive open-air meeting.
The left claims Fox played a part in election fraud which it says cheated Lopez Obrador of the presidency.
Antonio Fernandez, a pensioner, said: “Fox betrayed the Mexican people. That is unforgivable. Lopez Obrador is my president.”
The left claims Fox played a role
Mexico’s election court rejected the fraud claims and Calderon is due to take office on December 1.
Mexico has also said it is considering breaking off diplomatic relations with Venezuela after its president, Hugo Chavez, echoed the fraud allegations.
Chavez said in Caracas last week that his government had not recognized Calderon’s victory because of concerns about alleged irregularities.
He apparently expanded on his allegations Saturday when interviewed by CNN at the Non-Aligned Movement summit in Havana.
A CNN anchor said Chavez accused Mexico‘s ruling party of stealing the presidential elections, and that he said Calderon had “destroyed” the opportunity for good relations with Venezuela during his campaign.
In a statement emailed to reporters the Mexican foreign ministry said: “The Mexican government regrets this statement by the Venezuelan leader about a subject that pertains exclusively to Mexicans and their institutions.”
“In light of these statements, the Mexican government is evaluating the level of relations it will maintain with the government of Venezuela for the rest of this administration.”