Demand for tickets was so high that the singer’s own website, as well as some of the ticket sellers, crashed as people tried to log on.
She said: “I’m completely overwhelmed by the response to the shows. Thank you so much to everyone. Looking forward to seeing you all later this year”.
The singer’s PR company told fans on Twitter: “Tickets for all 22 @KateBushMusic dates sold out in less than 15 minutes.”
The London gigs mark the singer’s return to the stage 35 years after her one and only tour and to the same venue, the Hammersmith Apollo, where she effectively retired from live performances after just six weeks on the road in 1979.
She was just 20 when she completed The Tour Of Life with three dates at what was then called the Hammersmith Odeon, after topping the charts with Wuthering Heights the previous year, becoming the first woman to go to number one singing one of her own songs.
Over the years, theories about her absence from the stage have included her perfectionism, a fear of flying and the death of one of the tour crew, lighting director Bill Duffield, during a show.
But in a rare interview with Mojo magazine in 2011 to mark a comeback from one of her lengthy recording silences, she explained that her years of absence from the touring circuit were simply down to the sheer exertion of the ordeal. Her shows relied heavily on dance and mime.
“It was enormously enjoyable. But physically it was absolutely exhausting,” she said.
“I still don’t give up hope completely that I’ll be able to do some live work, but it’s certainly not in the picture at the moment because I just don’t quite know how that would work with how my life is now.”
For long periods she has largely withdrawn from public life to bring up her son, Bertie.
Her reappearances have been sporadic. Her 2005 album Aerial was her first release for 12 years, although in recent years her work rate has become a little more prolific with a collection of reworked songs from earlier albums called The Director’s Cut, as well as a themed album of songs about snow.
Last year she was awarded a CBE for her services to music.