Sainsbury's Local will occupy the former Lendlease sales suite on the ground floor of the One the Elephant development, next door to Pret a Manger.
A licence application for the new store has been submitted to Southwark Council for the new Sainsbury's store.
Plans submitted with the application show a convenience store layout with six self-checkouts and two staffed till positions.
Last year we reported on a petition launched by local residents calling on either Waitrose or M&S to occupy the empty shop unit. More than 300 people signed the petition.