The development will see three villages created across an area 1.5 miles wide.
At the heart of the site, which is three times the size of Hyde Park, will be a new market square with shops, bars and restaurants as well as office space.
The plans by Landsec include a large education campus with both secondary and primary schools, serving the growing Garden City population.
A third of the development area will be open space, and a large urban park will be formed to help integrate the former chalk quarry with the new homes.
Ian Piper, chief executive at Ebbsfleet Development Corporation which is overseeing delivery of the Garden City, said: “We are determined to create a great place for people to live within the Garden City and we will continue to work with all the developers to ensure the highest quality development is now delivered.
“The Development Corporation will invest further in key pieces of infrastructure, including an upgraded public transport network with dedicated routes for buses – meaning the majority of residents living in Eastern Quarry will be within a five minute walk of a bus stop – giving great connections across and through the Garden City.”
Ian Rickwood, chief executive of Henley, which is delivering the infrastructure for the scheme through Henley Camland, said: “We are pleased that planning permission has been granted for Eastern Quarry, which marks a significant milestone in progressing this landmark residential development in the heart of Ebbsfleet Garden City, and is testament to the strength and high quality of the plans.
“This project is in line with Henley Camland’s ongoing commitment to placemaking and creating communities, as well as contributing to alleviating the UK’s housing shortage through the delivery of much-needed new homes. We look forward to making further announcements in the near future on the successful momentum we are seeing at this site.”