"The circumstances in which I find myself assuming office today as acting president of our country are uncommon, sober and reflective," he said.
"More than ever therefore, I urge all Nigerians as a people of faith in God, to pray fervently for the full recovery of our dear President and his early return."
Al Jazeera's Yvonne Ndege, reporting from the capital, Abuja, said the decision by the national assembly had been backed by the 36 powerful governors controlling Nigeria's states.
"This comes after a very, very long and controversial absence of President Umaru Yar'Adua, who left Nigeria on November 31 on indefinite sick leave, without informing the national assembly and without and passing presidential power to the VP.
"What they have done amounts to a coup plot. It is a desperate decision by desperate politicians who were trying to save their face."
Festus Keyamo, constitutional lawyer
"It's been argued since his absence that this is in contravention of the Nigerian constitution of 1999."
It was not immediately clear if the parliamentary vote to hand over power to Jonathan had legal sanction, with no provisions in the constitution for the national assembly to take such a step.
Festus Keyamo, a constitutional lawyer, said the move was illegal.
"What they have done amounts to a coup plot. It is a desperate decision by desperate politicians who were trying to save their face," Keyamo told the AFP news agency.
Nigeria's constitution says the president must make a written declaration that he is on vacation or unable to carry out his duties before a transfer of power can take place.
Yar'Adua has been receiving treatment for a heart condition in Saudi Arabia since last November.
The senate said it based its decision on a January 12 interview with the BBC, in which the president said he would return to work once his doctors cleared him.
"We came to the conclusion that the president, through his declaration transmitted worldwide on the BBC, has furnished this parliament with irrefutable proof that he is on medical vacation ... and has therefore complied with the provision of section 145 of the 1999 constitution," David Mark, the senate president, said.
"The last 78 days have been very challenging to us as a nation ...however we have examined all options available to us and today rightly concluded it is necessary to take this stance to allow this country to move forward," he said.
Yar'Adua's absence has caused a ceasefire with fighters in the oil-rich Niger Delta to unravel and had left no one formally in charge of the nation of 150