Plans were approved in late 2009 for a garden centre in the car park, but were resubmitted after Jempson's asked for the 12,000 sq ft centre to be attached to the store itself. As part of the plans, the petrol station and forecourt Express store will also be relocated.
The energy-efficient Home & Garden Centre will feature a 150-seat restaurant and the new petrol station will have 50% more fuel pumps along with a new car wash and two further jet washes.
The supermarket will also be overhauled to create more and wider aisles, a larger local food and bakery section and a new till area.
"The redevelopment of our Peasmarsh site is a massive opportunity to enhance the shopping experience of our customers even further," said joint director Andrew Jempson.
Joint director Stephen Jempson added that the new centre was only the start of the retailer's plans.
"We intend to invest heavily not only in our Peasmarsh superstore, but in our Jempson's Budgens supermarkets in Rye and Hawkhurst and the café in Bexhill-on-Sea," he said.
The planning approval comes a week after Jempson's main supplier, Nisa-Today's, revealed its intention to supply more garden centres following success with a concept food store within a garden centre in Boston, Lincolnshire.