Jonathan had been fulfilling presidential duties since February. Yar'Adua died Wednesday in Nigeria's capital of Abuja after an extended illness. He was 58.
Jonathan will appoint a deputy and serve out the remainder of the presidential term until elections next year, the BBC reported Thursday. He was sworn in before government ministers and other officials at the presidential villa in Abuja about 12 hours after Yar'Adua's death.
Jonathan said his administration would focus on good governance, election reforms and fighting corruption, the BBC reported.
"One of the true tests will be that all votes count, and are counted, in our upcoming presidential election," Jonathan said.
Yar'Adua was to be buried in a Muslim ceremony Thursday in his home state of Katsina, officials said. He had been absent from politics since November when he went to Saudi Arabia for medical treatment that lasted several months.
At the time, a presidential spokesman said Yar'Adua was treated for acute pericarditis, an inflammation of the heart lining.