Born in Tokyo as the son of a shinpa actor, Inagaki appeared on stage in his childhood before joining the Nikkatsu studio as an actor in 1922. Wishing to become a director, he joined Chiezō Kataoka's Chiezō Productions and made his directorial debut in 1928 with Tenka taiheiki. Returning to Nikkatsu, he continued making jidaigeki and participated in the Naritaki Group of young filmmakers such as Sadao Yamanaka and Fuji Yahiro who collaboratively wrote screenplays under the made up name "Kinpachi Kajiwara". Like others in the group, Inagaki was known for his cheerful and intelligent samurai films. Inagaki later moved to Daiei and then Toho, where he made big budget color spectacles as well as delicate works depicting the feelings of children. He also produced many films and wrote the scripts for dozens of others.