The appointment of Odumosu, a former Commissioner of Police in Lagos state is subject to senate confirmation.
This comes after the suspension of Abdulrasheed Bawa as anti-graft agency boss.
He retired from the Nigeria Police Force in January 2022, shortly after his elevation to the rank of Assistant Inspector General (AIG) and after serving for 32 years.
Meanwhile, Bawa was suspended last week by President Tinubu following allegations of corruption against him.
Bawa’s suspension is “to allow for proper investigation into his conduct while in office. This follows weighty allegation of abuse of office leveled against him.
“Mr Bawa has been directed to immediately hand over the affairs of his office to the Director, Operations in the commission, who will oversee the affairs of the Office of the Chairman pending the conclusion of investigation,” a statement from the presidency read.