Under the constitution, Jonathan is now the head of state until the country's next elections scheduled to be held by April 2011. He will also nominate a vice-president, subject to approval by the senate.
In his acceptance speech after taking the oath, Jonathan said his coming to power had occured under "very sad and unusual circumstances".
He praised his predecessor as a "man of great personal integrity ... and outstanding humility" and he said he would continue the fight against corruption and push for electoral reform during his time in office.
"Our total commitment to good governance, electoral reform and the fight against corruption would be pursued with greater vigour."
"Similarly the effort at ensuring the sustenance of peace and development in the Niger Delta as well as the security of life and property around the entire country would be of top most priority in the remaining period of this administration."
Yar'Adua had failed to formally transfer his powers to Jonathan while he was in Saudi Arabia earlier this year, sparking a constitutional crisis in Nigeria, Africa's most populous nation with 150 million people.
Yar'Adua returned to Nigeria in February after three months of medical treatment in Saudi Arabia, but had not been seen in public since.
Al Jazeera's Yvonne Ndege said the severity of his illness had been shrouded in secrecy since he was airlifted out of Nigeria in November 2009.
"He had always suffered some kind of sickness since becoming president, he had had kidney problems and the latest bout of illness was related to a heart condition," she said.
"There were so many local media reports that he was on the mend but we will never really know the true extent of his illness except that he had been terminally ill."
The National Assembly left open the possibility for Yar'Adua to regain power if he returned to the country in good health. But his long absence from public life and the secrecy surrounding his health sparked months of fierce speculation in the Nigerian media and constant tension between his supporters and those of the acting president.
Jonathan, meanwhile, has consolidated his power, appointing a new cabinet and his own team of advisers.
|Yar'Adua's absence had sparked fears of a power vacuum in Nigeria [AFP]
Abba Aji, a senator and special adviser to Yar'Adua on national assembly matters, told Al Jazeera he had no objection to Jonathan continuing as president and contesting in next year's presidential election.
"I certainly have no problem with this [arrangement] but the ultimate decision as to who will be the next president will have to be made by the Nigerian electorate … as of right every Nigerian has the right to contest the election."
It is unclear if Jonathan, who is from the mainly Christian south of Nigeria, will run for president in the polls because of an unwritten agreement in the ruling party that power rotates between north and south.
Under the agreement, the north, where Yar'Adua hails from, theoretically has another term in office following his death.
'Dicey' transition period
Nii Akuetteh, the former executive director of Washington-based think tank Africa Action, told Al Jazeera that Yar'Adua pushed through electoral reforms and will be remembered as a clean president.
"When a president dies suddenly, the transition period is always dicey.
"On the other hand, his health has been bad for a long time so the Nigerian power structure has had time to prepare for this.
"I think it will be a fairly smooth transition. I don't expect any kind of upheaval since Jonathan as acting president is already firmly in control."
Yar'adua took office in 2007 in a country notorious for corruption and was praised by many for being the first leader to publicly declare his personal assets when taking office - setting up a benchmark for comparison later to see if he misappropriated funds.
Andrew Simmons, Al Jazeera's Africa editor, said the death of Yar'Adua had been no surprise coming after a long illness, but it was nonetheless a tragic end to what could have been a promising presidency.
"Yar'adua, a former chemistry teacher, was taciturn, down-to-earth but who was just underestimated initially. The one thing that stood in his way was his health."
Simmons said the Nigerian leader left a legacy of a clean government which included transparency, electoral reforms and an amnesty with militants in the oil-rich Niger Delta.
"He did not achieve many of the reforms he promised mainly because his health had got in the way … but he had achieved something."