The swearing-in ceremony in the capital, Abuja, also saw President Tinubu's allies elected as Senate President and House Speaker, to mark the official start of legislative duties for newly elected officials.
Tinubu has up to the end of July to name his cabinet but his aides say the president could submit some names as soon as next week. His choice of finance, petroleum and defense ministers as well as national security adviser would be closely watched.
Nigeria's Senate wields significant influence in Nigeria's bicameral legislature, including scrutinizing and confirming the president's cabinet nominees.
Tinubu's ruling party controls a majority in both arms of the national assembly - and political analysts say this will make it easier for the president to push his legislative agenda.
The 71-year-old Tinubu suspended central bank governor Godwin Emefiele last week, cheering markets, but his permanent removal would require a vote by the Senate.