The final curtain will fall on the multi award-winning show at the Victoria Palace Theatre on 9 April.
The story about the miner's son who dreams of becoming a ballet dancer is leaving to allow for the theatre's refurbishment, announced last year.
But fans of the production will not be left bereft as it will be embarking on its first tour of the UK and Ireland.
The theatre's makeover comes after it was bought by stage impresario Cameron Mackintosh, which is also part of extensive redevelopment work that is taking place around Victoria station.
The first regional Billy Elliot shows will begin in Plymouth in February before stops around cities including Sunderland, Bradford, Cardiff, Edinburgh and Dublin, with dates currently planned until May 2017.
The Victoria Palace has been the musical's home since it first opened to great fanfare, following the acclaim achieved by the Oscar-nominated film on which it is based and the big names involved in bringing it to the stage.
The film's director, Stephen Daldry, was part of the show's creative team along with Sir Elton John, who wrote its score.
"Billy Elliot has been one of the most rewarding experiences of my entire life. The talented young performers who have become part of our Billy Elliot family have amazed me with their achievements from the very start," Sir Elton said.
"I am so delighted that new audiences around the country will now have the opportunity to experience this extraordinary piece of work."
Daldry and the show's lead producer, Eric Fellner, said they knew it would have to leave the Palace theatre at some point - but had not anticipated it would run as long as it has.
"We knew when we did the original deal that we would leave one day but we had no idea it would be 11 years on," Fellner told the Daily Mail.
He also confirmed plans for a film version of the musical were "chugging along", although he added it was realistically "three or four years away".
The musical has been seen by more than 5.25 million people in London and nearly 11 million people around the globe in worldwide productions.
Billy Elliot the Musical is to close in London after 11 years and 4,600 performances.