The Royal Parks are trying to make better use of its buildings including the 245-year-old Magazine building, which will be the new gallery.
Zaha Hadid - the Pritzker-prize winning arch modernist architect - will redesign the Grade II listed building overlooks the Serpentine Bridge.
Plans include an adjoining pavilion to be used as a social space and restaurant. Serpentine Gallery will pay royal Parks £300,000 a year to rent the building.
It is due to open in time for the London 2012 Olympic and Paralympic Games, and the 880sqm gallery is to the Serpentine Gallery’s footprint.
Royal Parks chief executive Mark Camley said of the newly-named Serpentine Sackler Gallery: "We are bringing this building into public use for the first time.
"Income from the licence will be invested into the Royal Parks. Given the challenging times that lie ahead, this is positive news."
Serpentine Sackler Gallery Dr Mortimer and Theresa Sackler Foundation gave the largest single gift the Serpentine Gallery has received in its 40 year history.
Julia Peyton-Jones, co-director of the Serpentine Gallery, said: "We have been interested in the potential of the building for some time.
"In these challenging times we feared the opportunity would be lost. We are very grateful to our long-term friends for their very generous assistance."
Cost of the redesign has not been disclosed but will depend on a big donation by the Dr Mortimer and Theresa Sackler Foundation.