The broadcaster is in the process of vacating the iconic West London site which it has sold to property developers.
BBC Worldwide and BBC Studios and Post Production will retain a small presence on the site, and the BBC is expected to be one of several production companies who will use the refurnished main studios.
The rest of the site will be redeveloped to include a mix of leisure, office and residential space.
BBC Four’s night of programming will start with Madness taking to the stage in front of Television Centre to perform live in front of an assembled audience.
The concert will include new material and classics alike such as One Step Beyond, I Never Knew Your Name, Baggy Trousers and Our House.
Richard Klein, Controller BBC Four, said: “I can think of no better band than Madness to help celebrate a golden age of television coming out of the BBC’s Television Centre, and I am really pleased that one of Britain’s finest groups has agreed to come along and help BBC Four celebrate in fine style. Madness, as always, are one step beyond!”
Madness said: “We’ve played at some exciting places in London lately but the closing of BBC TV Centre… well… that is close to our hearts, as a band we grew up there, those walls have plenty of Madness tales to tell, a sad day… the end of an era…. oh, but what a celebration! We’re honoured to be the band the Beeb have chosen for this fond farewell.”