He wore a red-white-and-green sash like those of Mexico's presidents as he told his supporters in Mexico City on Monday that his "legitimate government" would work for the poor.
"No matter how cynical he is, he can not feel secure. Calderon is the lowly servant of the white-collar criminals."
Federal police have already set up barricades around the chamber of deputies to prevent Lopez Obrador's supporters from setting up new protest camps before Calderon's inauguration ceremony on December 1.
Followers of Lopez Obrador's Democratic Revolutionary Party have threatened to disrupt the ceremony, saying that the election was won by fraud and that the president-elect "is undeserving of any respect or consideration".
The launch of the opposition government was timed to coincide with the anniversary of the 1910 Mexican revolution, when Francisco Madero, Emiliano Zapata and Pancho Villa took up arms against conservatives to found modern Mexico.
The former mayor of Mexico City has encouraged supporters to donate to his alternative administration on his website.
Since Calderon was announced the winner, Lopez Obrador and his supporters have carried out a number of demonstrations to protest against the decision but much of his support has faded since the courts refused to overturn the result.
A poll in the Reforma newspaper on Monday indicated that 56 per cent of those questioned opposed his decision to name himself "legitimate president" while 19 per cent supported him.