The £95 million development on the Glen Road will also include a hotel, retail centre, office premises, a play park and two care homes.
Sinn Féin MLA Pat Sheehan welcomed planning approval for one of the largest housing developments in Belfast since 2000.
The West Belfast MLA said: "I welcome planning approval by Belfast City Council for one of the largest housing developments in Belfast in the last 20 years. The development will be located at the Glenmona site which is conjoined to the Monagh By-Pass in West Belfast.
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"The project will see the construction of 656 homes, 550 of which are social and 106 affordable. The homes will be a made of a variety of semi-detached, detached, townhouses and apartments.
"There are many families and workers in West Belfast that have spent years on the housing waiting list, an unacceptable reality and one that Sinn Féin have been working actively to address.
"Housing is a fundamental human right that must be enjoyed by all.
"Myself, Paul Maskey MP and Cllr Ronan McLaughlin have been consistently meeting with the Braidwater developers over the course of the last year on this development to ensure that the needs of our community in West Belfast are met and we will continue to do so in the time ahead.
"This development will also result in the creation of hundreds of short-term employment opportunities during construction and long-term opportunities with the retail units, hotel, office premises and two care homes."
