Demonstrators are unlikely to reach Congress - which has been surrounded by police and presidential guards - but he is expected to face a hostile atmosphere when he steps inside the building.
Politicians from Lopez Obrador's Democratic Revolution Party, the PRD, had fought with MPs from the ruling party for control of parts of the podium on Tuesday, then staked out their territory by camping out with blankets and pillows for three days, in a bid to block the ceremony.
'A better Mexico'
Calderon used the televised ceremony to call on politicians from both sides to respect the constitutional process, saying: "I invite you to build a better, different Mexico, a winning Mexico."
He also pledged to "be the president of all Mexicans, without distinction, without regard to a person's political preferences".
"I have received the presidential offices from President Vicente Fox, the start of the process of taking possession of the presidency," Calderon said. "Later, I will appear before Congress to take the constitutional oath."
In what a voice-over narration called "a symbolic ceremony", Fox handed the badge of office - a sash - to a military officer; Calderon will receive it later on Friday when he takes the oath in Congress. In the past, incoming presidents have waited until the inauguration to make a speech.
"I am not unaware of the complexity of the political times we are living through, nor of our differences," he said.
"But I am convinced that we today we should put an end to our disagreements and from there, start a new stage whose only aim would be to place the interests of the nation above our differences."
Tensions have been high in Mexico since Lopez Obrador lost the July 2 election by less than one per cent. After the result was announced he claimed Calderon had won through fraud and led weeks of protests.
Last week he chose a cabinet and declared himself the legitimate president of Mexico.