River Reign will play each Thursday at the restaurant on the corner of Victoria Ave and Ingestre St, and will be joined by guests from time to time.
Keyboardist Chris Dann and bassist Phil Ponga complete the line-up.
River Reign describe themselves as "four men with a wealth of musical experience playing diverse idioms" and say listeners can expect "melodies, harmonies, polyrhythms and daring improvisations".
Mills said they were unsure how the idea might develop - "Nobody else is doing it, not the style or the level we are doing it.
"I want people to listen - we are a band to listen to."
River Reign will play at Angora between 8.30pm and 11pm. Restaurant customers can stay on for the music, while there is a $5 door charge for those who come for the music with a listener's menu at the bar.