The application was put forward by the Flagship Group.
The project is designed to bring meaningful, long-term change and improvements to the Abbey and increase the supply of much-needed affordable homes. It would take place in phases over 20 years.
Peter Hawes, Flagship Group's Chairman, said: "This is an exciting day for the Abbey, which has been at the heart of the Thetford community since it was built more than 50 years ago.
"The outline planning application follows five years of talking to the people who have a home on the Abbey.
"Local people have told us that they do want to see improvements for the Abbey and they’ve let us know what things could be better."
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The Abbey has around 1,100 homes and Flagship hopes to improve and retrofit some existing homes while replacing others with new homes, built to a high standard. The new homes will also be far more energy-efficient.
The plan also seeks permission for an additional 320 to 500 homes - although this figure is yet to be confirmed and will be based on further consultation.
Flagship's vision includes improved parking, lighting, pavements, play areas and green spaces.
The Abbey will get a new neighbourhood 'heart' with a neighbourhood park and community centre. There will be better and safer walking and cycling routes to the town centre, Little Ouse riverside and Thetford Forest.
Mr Hawes added: "We are still at an early stage. The application is just for the principle of change for the Abbey and doesn’t set out the details of what would happen.
"A regeneration project of this size must be delivered in multiple phases.
"Each phase of the detailed design will be informed by local people, through further consultation, with separate reserved matters applications submitted at each stage.
"Flagship has never undertaken a project with more engagement and consultation than this - but this is still the beginning.
"We're going to keep listening and speaking to residents in the weeks, months, and years to come."
The Group plans to fund an independent tenants and leaseholders advisor to act as a "resource for the community" as the plans progress.
