Tinubu was sworn in at a ceremony at Eagles Square, in the capital Abuja, attended by local and foreign dignitaries.
Two of Tinubu’s main opponents in the February election are challenging his victory on the basis of fraud claims. A tribunal will start on Tuesday to hear their main arguments, with a ruling not expected before September.
Buhari, a taciturn former military ruler, leaves Africa’s biggest economy and most populous nation deeply divided.
The election had galvanised young voters hoping for a break from the two parties that have dominated Nigerian politics since military rule ended in 1999. But what authorities promised would be the country’s freest and fairest election yet ended in frustration for many.
Tinubu, a member of Buhari’s All Progressives Congress who has long exerted influence from behind the scenes, won with 37% of the vote, the lowest share since 1999.
(Reporting by Felix Onuah in Abuja and MacDonald Dzirutwe in Lagos; Additional reporting by Chijioke Ohuocha in Abuja; Editing by Alexander Winning and Mike Harrison)