The new service chiefs include a former anti-corruption boss, Mallam Nuhu Ribadu, as national security adviser.
Major General C.G Musa, who was in charge of fighting a jihadist insurgency in the country's north, has been named chief of defense staff.
Replacing key staff is common for new Nigerian presidents, but Tinubu had promised to make security a priority as the country grapples with violence in several regions.
A presidential statement issued late Monday said Tinubu made the appointments after sacking all the incumbent military service chiefs and advisers, as well as the national police chief and head of the customs service, "with immediate effect."
Security is a major concern for Nigerians, who face a 14-year-old Islamist insurgency in the northeast, heavily armed criminal kidnap gangs in the northwest and separatist tensions in the southeast.
Last week, the president sacked the central bank governor, Godwin Emefiele, as well as the head of the anti-graft agency, to help consolidate his new administration.