The £7m Aldi project is on the site of a former car showroom.
The German budget supermarket is a growing competitor among British supermarkets.
Rother councillors have given the green light to a new Aldi store in Rye, which currently has just one supermarket.
Jempson's, which operates Rye's only existing large supermarket, has opposed the planned Aldi store.
Aldi wants to build a supermarket on a green space used by a local rugby club for youth training.
The industry data suggests that despite Asda embarking on a turnaround, it has been losing ground to rivals.
Aldi is asking residents to share their feedback on the proposal for a new store.
New locations include Southam in Warwickshire, Hastings in Sussex, and Amersham in Buckinghamshire.
A council reconsiders its planning permission for an Aldi supermarket after a challenge from Lidl.
