Madness will perform live in the front of BBC Television Centre as part of an evening of entertainment bidding farewell to the iconic building.
Celebrating its 53 year history, BBC Four will produce the hour-long programme to be shown on 22 March, nine days before TV Centre closes its doors.
Coldplay and Beyonce have performed in the car park in past years.
Madness, whose hits include One Step Beyond, said they are "honoured" to be part of this "fond farewell."
A statement from the ska act, who rose to prominence in the early 80s, read: "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."
The band will play new material from their recent tenth studio album Oui, Oui, Si, Si, Ja, Ja, Da, Da alongside the hits Baggy Trousers, I Never Knew Your Name and Our House.
The transition to the BBC's new London home, the central New Broadcasting House, began in October last year.
The 1960s building in west London, once home of Top of the Pops and Blue Peter and sold for £200 million, closes on 31 March and will be redeveloped into hotels, flats, a cinema and office space.
The main television studios will be retained and refurbished for leasing out to production companies, including the BBC, from 2014.
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.
"I am really pleased that one of Britain's finest groups has agreed to come along and help BBC Four celebrate in fine style."
The concert will be followed by a two-hour special, pre-recorded on 18 March, called Goodbye TV Centre.
Hosted by former BBC chairman Michael Grade in front of a studio audience, it will feature interviews with the likes of Sir David Attenborough, Ronnie Corbett, Noel Edmonds, Sir David Jason and Sir Terry Wogan.
Thinking of buying something on Amazon? Kindly use the link below: