One of Jonathan's first tasks may well be answering claims that some of his police force were involved in extra-judicial killings.
The evidence, on video, was obtained exclusively by Al Jazeera.
In his first major step, Jonathan removed Michael Aondoakaa, the powerful justice minister, on Wednesday.
Aondoaka, who was also the country's attorney-general, had been among the group of ministers who held out most strenuously against formally transferring power to Jonathan during Yar'Adua's absence of more than two months.
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 not officially given his consent to the move.
The senate, in voting on Tuesday, said it based its decision on an interview with the BBC last month, in which the president said he would return to work once his doctors cleared him.
Last month a court ruled that Jonathan could exercise presidential functions but not as an acting president.
Part of the political battle in Nigeria is the delicate regional balancing act: Yar'Adua is from the Muslim north and Jonathan from the Christian south.
The presidency traditionally switches between the two sides at every election. But in recent weeks the regional power battle has taken a back seat with governors from the 36 states rallying behind Jonathan.
Chairman of the governors' forum Bukola Saraki said Tuesday's move by parliament "shows that definitely the democracy of this country has matured and shows that we have courageous democrats [in parliament]".