Jonathan took the oath of office in front of government ministers, state governors and ambassadors at the presidential villa in Abuja almost 12 hours after Yar'Adua died, aged 58, following a long battle with kidney and heart ailments.
Jonathan had already been running Africa's most populous nation as acting president for several months while Yar'Adua was incapacitated.
He will appoint a new deputy and the pair will then complete the unexpired presidential term in the oil-producing nation of more than 140 million people until elections due by April 2011.
"Nigeria has lost the jewel on its crown," Jonathan said before the ceremony, announcing seven days of national mourning.
Yar'Adua was buried in his northern home town of Katsina on Thursday.
Yar'Adua had been absent from the political scene since November, when he left for medical treatment for a heart condition in Saudi Arabia. He returned to Nigeria in February but remained too sick to govern.
Jonathan assumed executive powers in February and has since consolidated his hold on power, appointing a new cabinet and his own team of advisers. But Yar'Adua's death raises the stakes in the run-up to the next election.
It is unclear if Jonathan, who is from the southern Niger Delta, will run for president because of an unwritten agreement in the ruling party that power rotates between north and south. The next four-year term is due to go to Yar'Adua's Muslim north.
"The paramount issue will be who the new vice-president will be. It'll probably be a northerner (who) will be front-runner for the presidency in 2011," said Kayode Akindele, a director at Lagos-based consultancy Greengate Strategic Partners.
Yar'Adua was Nigeria's first university-educated leader and won in the April 2007 polls which, though marred by intimidation and ballot-stuffing, marked the first transfer of power from one civilian president to another since independence in 1960.
His biggest achievement was in the restive Niger Delta, the heartland of Africa's biggest oil and gas industry.
Militant attacks rumbled on during the early part of his tenure, but his offer of amnesty last year led thousands of gunmen to lay down their weapons and has brought more than six months of relative peace in the region.
Reuters
(China Daily 05/07/2010 page12)