The appointment followed a recommendation by the University Joint Council and the Senate selection Board to the governor.
Mr Garba, 56, is to succeed Suleiman Dangoggo, a professor of Chemistry whose five-year tenure ended this year. Mr Dangoggo was appointed the VC in 2017.
Governor Tambuwal also approved the appointment of Kuluwa Abubakar Nuhu as the new Registrar of the state university.
Mrs Nuhu, for her part, is best known as a seasoned university administrator and former Commissioner for Women Affairs and Deputy Registrar at the Office of the Vice-Chancellor of Usmanu Danfodio University, Sokoto.
According to a statement by Muhammad Bello, the special adviser to Mr Tambuwa on media and publicity, both appointments are with immediate effect.