The first stage plan includes a 3,500-capacity indoor arena, a digital square, hotel and car park on the leisure centre car park site and a foot bridge over Oystermouth road.
The second phase includes shops, restaurants, cafes and a cinema on the former St David’s shopping centre site.
Outline permission was granted in June.
It is hoped the first phase will be up and running by 2020 and will be a “catalyst” for other city centre sites.
The council said current proposals to cut funding to its regeneration department by £280,000 will not hamper efforts to transform the city centre.
Council leader Rob Stewart said the development was “vitally important to the city centre”.
He said: “It’s important that local firms are part of the development so that the jobs local people need are created locally and the money we spend on building our new city stays within and benefits the region.
“These new jobs will contribute to the 35,000 new jobs we plan to create from the Swansea Bay City Deal and other projects.”
Ambassador Theatre Group has been appointed to run the digital indoor arena, which will attract up to 200 days of concerts, exhibitions and other events every year.