It marks the first phase of Plasdwr, a 900-acre site bordering Fairwater, St Fagans, Danescourt and Radyr.
Work is expected to start to the north and south of Llantrisant Road in the summer and the first residents are expected to move in by spring 2017.
Construction of the first phase of the garden city will generate between 2,000 and 3,000 jobs, Redrow Homes said.
The developers said Plasdwr would include shops, schools, leisure centres, pubs and restaurants.
The first 630 of 7,000 homes planned for a £2bn garden city in Cardiff have been given the go-ahead.