Property developer Murray Estates plans to build the homes at Gogar as the first phase of its £1 billion 600-acre Garden District scheme.
Overall, proposals include developing more than 6,000 new homes, a school, community facilities and a shopping complex.
However, while councillors voted 35-17 in favour of the project's first phase, the Scottish Green Party has criticised the decision.
-- Advertisement --
Green Councillor Steve Burgess said there were "very significant reasons" for refusal, "on transport, on the environment and on the integrity of the planning system".
He added: "It is very clear that the development will increase car use, congestion and air pollution. It is clear that cyclists' and pedestrians' needs have been ignored. And the development sacrifices a green belt which has served the city for over half a century.
"And, finally, it does not serve to meet the city's pressing need for affordable housing in well-connected places. The additional housing demands of the city are almost entirely from older and single person households. Adding to suburban sprawl does nothing to meet their needs."
The application will now be submitted to the Scottish Government for consideration.
(LM)
