The planning application was submitted jointly by developer Urban & Civic and trusts associated with Nuffield College, Oxford .
The proposed 162-hectare Wintringham extension includes two new primary schools, health facilities and 63,000 m2 of new employment space as well as housing.
Urban & Civic acquired a 33% interest in the project for £13.3m in April 2017 and has taken on master developer role. Terms have been agreed for the first parcel and the target is for first occupations by November 2019.
Urban & Civic chief executive Nigel Hugill said: "Last night's decision demonstrates exactly what can be achieved when a master developer and a committed local authority work positively together. The application, including almost 3,000 new homes, was determined within 20 weeks. That must be a record. In 30 years of large scale development, I have never known a new strategic application being determined so expeditiously. First plot sales will be under the now established Urban & Civic licence model and are well advanced. We are working towards initial occupations within two years of application submission. The historic average on major residential projects is almost seven years."