The film's director, Robert Zemeckis, has teamed up with the people behind theatrical hits including Wicked and Ghost to develop the show and hopes to open it in London in 2015 - 30 years after it was first shown in cinemas.
Michael J Fox played teenager Marty McFly, who travels back in time to his parents' schooldays, in the 1985 film which was a huge worldwide hit and sparked a money-spinning movie franchise.
Bob Gale, who co-wrote the original films with Zemeckis, said: "The Back To The Future Musical is a project that Bob Zemeckis and I have been exploring for almost 10 years. We're thrilled to be at last in partnership with a creative and producing team that will create a show that is true to the spirit of the film without being a slavish remake."
He added: "We intend to use music from the movie along with brand new songs to make a version of Back To The Future that is fresh, entertaining and takes advantage of all the amazing things that can now be done on stage. We can't think of a better way to celebrate the 30th anniversary of the film."
The team has also signed up a skateboard consultant to help recreate the scene where Fox's character accidentally invents the craze.