The correspondence is the first from Mr Tinubu to the Senate since he assumed office as Nigeria's president on 29 May.
President Bola Tinubu has asked the Senate to approve him appointing 20 special advisers to run his administration.
The request was contained in a letter read by the Senate President, Ahmad Lawan, at the plenary session on Tuesday.
The correspondence is the first from Mr Tinubu to the Senate since he assumed office as Nigeria's president on 29 May.
In the letter, the president was silent on the names of the people he wanted to appoint as special advisers and their portfolios.
After it was read, the Senate Leader, Ibrahim Gobir (APC, Sokoto East), moved that "the Senate do consider the request of Mr. President and C-in-C for the approval of the Senate to appoint 20 Special Advisers."
The Senate Minority Leader, Philip Aduda, seconded the motion.
The Senate, therefore, approved the president's request to appoint the 20 special advisers.
Mr Tinubu recently appointed a former Benue State governor, George Akume, as secretary to the government of the federation (SGF) and the Speaker, House of Representatives, Femi Gbajabiamila, as his chief of staff.
The current ninth Senate will wind down next week. Thus, subsequent appointments by Mr Tinubu will be considered by the 10th Senate, which will be inaugurated on 13 June.