The RA announced that cars would eventually be banished from the Burlington House courtyard to make way for a stone-paved piazza offering "a place of calm and unity".
Upon entering the courtyard, visitors will be greeted immediately by the statue of Sir Joshua Reynolds, the founding president, moved 70 feet forward from the spot he has stood in since 1931.
The redesign has been made possible by an "very generous" donation from the American philanthropist, 91-year-old Walter H Annenberg, a media magnate and a former American ambassador to Britain.
"The Annenberg Courtyard is the Royal Academy's millennium gift to London," said Sir Philip Dowson, the president of the RA.
Yesterday the RA revealed the new courtyard, to be designed by Sir Michael Hopkins, would be used for an innovative programme of exhibitions of contemporary sculpture.
Dr Tom Inch, the chairman of the Burlington House secretaries' committee, said: "The development will provide a more appropriate setting for the Renaissance-style architecture of the buildings and the surrounding courtyard."
Dr Inch added that the committee had agreed with the Department of Environment, Transport and the Regions - which owns the courtyard - to limit traffic and cut permanent parking by half next January with a view to stopping it after two years.
Work on the redevelopment will start in the new year.
The RA was given a 999-year lease to Burlington House, Piccadilly, in 1867 at a peppercorn rent.