The musical will open for a 10-week run at the Hammersmith Apollo in June, with actors still to be cast.
It will be based on the first movie, which turned Zac Efron and Vanessa Hudgens into global stars.
Two High School Musical films have been made, with a third in production. A separate stage show is already touring UK theatres.
The first two movies were made for US TV, with the new installment aimed at cinemas.
The stories follow teenage couple Troy and Gabriella, played by Efron and Hudgens.
Disney executive Steve Fickinger said: "I think the reason High School Musical has been so successful is that kids really enjoy aspirational stories.
"Like Buzz Lightyear saving the day or Cinderella going to the ball, kids can really relate to that."
Disney has already enjoyed stage success in London with Mary Poppins and The Lion King.
The touring High School Musical show, which opens in Bromley, south London, on Monday, has already sold £9m in advance sales.
[source]