Minelli, who last performed at the venue in 1973, won an Oscar for playing Sally Bowles in Bob Fosse's film version of Kander and Ebb's musical Cabaret, which is set during the period.
She said: "I'm always so excited to perform in London. I have so many friends and fans there I consider it my second home. And to be returning to the Royal Festival Hall after all this time is thrilling; I remember bringing Liza with a Z there in the early 70s and having such a swell time. So I can't wait to see all you guys again."
The concert will see her perform songs from Cabaret, which will also be screened as part of the festival. Running as part of the year-long The Rest is Noise festival, the weekend commences on 1 March 2013.
Jude Kelly, artistic director of the Southbank Centre, said: "We are delighted to welcome back Liza Minnelli to the Royal Festival Hall to perform as part of our year-long The Rest Is Noise festival. Fosse's Cabaret is one of the most iconic, intimate depictions of 1930s' Berlin and we are thrilled that the artist who so brilliantly gave life to the complex character of Sally Bowles can take part as we look back at this particular moment in history."