Councillors have granted outline planning permission for the former Sainsbury's site in the city's Shaftsbury area.
A health centre, cafe and shop are also included in the plans for the 3 hectares (7 acre) plot.
A council report said it would bring "significant regeneration benefits".
Plans for a derelict supermarket site in Newport to be redeveloped into 600 student flats and a hotel have moved a step closer.