The restaurant, known for its gravy-dipped sandwiches and burgers, shut its doors in late July.
Dip & Flip was founded in Battersea in 2013 and is left with four remaining sites across south London, including Wimbledon, Tooting and a pop-up in Waterloo.
Bar brand Tequila Mockingbird has taken over the Brixton location, which will be its first site to serve food.
It is expected to open in September following a refurbishment.
Tequila Mockingbird has three other bars in Battersea, Putney and Tooting.
Advisors at CDG Leisure acted on behalf of Dip & Flip on the disposal of the Brixton site.