The Clerkenwell-based practice beat fellow finalists Feilden Clegg Bradley, Benson & Forsyth, Urban Salon and Keith Williams to win the RIBA-organised contest.
The RCA hopes the scheme will become a 'substantial second site', just two miles south of its main Kensington Gore campus, and will be used for teaching, research and business-related activities.
The judging panel included Spencer de Grey from Foster and Partners; Derek Walker of Derek Walker Associates; and a number of representatives from the RCA.
Speaking shortly after the shortlisting stage, Christopher Frayling, rector of the RCA, said: 'We had a terrific response to the competition and have selected a shortlist of five very varied practices.
'The college can now look forward, with every confidence, to working with a first-rate architect on the development of our much-needed North Site in Battersea: the competition has reached a very exciting stage.'