The impending arrival of the new supermarket has been revealed in an application to Southwark Council for advertisement consent for signage inside and outside the shopping centre.
A Co-op spokeswoman told the SE1 website: "We look forward to bringing our award-winning ranges to even more of customers and members later this summer with a new convenience store at the Elephant & Castle Shopping Centre."
Stafford Lancaster, investment director at Delancey, added: "Following Tesco's decision to close its store last month, we have been working very hard to attract a new supermarket, given our full commitment to ensuring the shopping centre remains a vibrant, thriving shopping location ahead of the redevelopment.
"We are delighted to welcome the Co-op to the Elephant & Castle Shopping Centre. As a quality, convenience supermarket it brings a great offering to the centre and the wider Elephant & Castle area.
"The installation of a new cash machine will further provide a useful facility for shoppers in the centre."
The Co-op will occupy the ground floor unit at the shopping centre previously home to Tesco Metro.
Tesco closed its store earlier this year amid a dispute with the centre's landlords about pest control.
Co-op is already hiring staff for its new branch, with adverts for store supervisors and customer team leaders currently showing on recruitment websites.
72 staff were affected by the closure of Tesco Metro.
Earlier this week the former Tesco space on the upper level of the shopping centre reopened as a temporary 'community hub'.
The Co-op has five convenience stores in SE1 already: Westminster Bridge Road, Southwark Bridge Road, Sumner Street, Tower Bridge Road and Dockhead.
The reopening of a supermarket in the shopping centre will provide a boost to other traders in the complex who have been hit by the loss of footfall since Tesco shut its doors.
A timetable for the winding down of the shopping centre ahead of redevelopment is still unclear, with a High Court challenge pending and construction work yet to start on the temporary shops on Elephant Road which must be built before the centre shuts.
• See details of the Co-op's new signage at 19/AP/1827