The inauguration took place in the capital Abuja at Eagles Square, with local and foreign dignitaries in attendance.
"As president of the Federal Republic of Nigeria I will discharge my duties and perform my functions honestly to the best of my ability, faithfully and in accordance with the constitution," Tinubu said in a live broadcast.
African leaders were at the ceremony, including the presidents of South Africa, Rwanda and Ghana. Delegations from the United States, the United Kingdom and China also took part.
The 71-year-old southerner won the elections that were held in February this year with 8.8 million votes, succeeding the 80-year-old Muhammadu Buhari who is also a member of the All Progressives Congress party (APC).
Sometimes referred to as a political "godfather," Tinubu has been known for exerting power from behind the scenes and using his extensive network to back candidates for office.
However, Tinubu only won the elections with 37% of the vote, the lowest share since 1999.
Accusations of rigged elections
While Tinubu bagged the required number of votes across two-thirds of states in Nigeria, two of Tinubu's main opponents have cried foul. They have challenged the election results on the basis of electoral fraud.
The hearing of the main arguments will commence on Tuesday, but the court's decision is not expected until September.
Nigeria's electoral commission admitted there had been "glitches" during the ballot but refuted claims that the elections were not free and fair.
Nigeria's economic and security challenges
During his tenure, Buhari had promised to resolve issues of corruption and insecurity but left many disappointed.
The country is reeling under economic distress that has resulted in two-decades of high inflation, record debt, weak currency, shortages of foreign exchange and fuel.
Violence is rampant in the country with separatists and gangs wreaking havoc in the southeast which has left many Nigerians feeling insecure.
The oil-rich nation also faces the major challenge of swapping crude oil worth billions of dollars for gasoline which it then needs to subsidize for its domestic market. This has contributed to ballooning debt.
The incoming government will also need to prioritize issues concerning security which have seen a significant rise in recent years.
rs, mf/kb (AFP, Reuters)