A final decision on the 12,000-capacity venue was put off by councillors earlier this month because of concerns about how people would get to and from it.
The planning go-ahead last night paves the way for Bouygues UK to begin work on the indoor venue later this year.
The new venue is due to be located on the derelict former diesel depot site, close to Temple Meads station.
International arena design team Populous together with Bath-based architects Feilden Clegg Bradley and engineering firm Buro Happold have developed plans for the innovative and flexible arena.
It will be financed by the council borrow £53m against its City Deal and raising the remaining £38m from the arena operator and car parking income.