Developer Morgan Davis Wherry said it would shortly invite tenders for the new building, which is expected to cost up to £10m to build.
It has committed to use a local demolition contractor and building firms where possible to boost local jobs.
The Newark based developer will build a 7,700 sq m supermarket with 440 parking spaces and petrol station on a two-hectare former Anglo Dutch Meat site in Arkwright Road, Hampden Park and will make local road improvements as part of the section 106 agreement.
The application received just five letters of objection from local residents who raised concerns about increased traffic and claimed another supermarket could unbalance the town.
Eastbourne MP Stephen Lloyd said, “I am particularly pleased that Morrisons have got in place a robust agreement with the local job centre to ensure we get new jobs for people in our town.
“In addition I negotiated an agreement with them to include local builders and construction sub-contractors.”