The show, which has been described by its director Rafael Alvero as a tragic opera, will feature a 22-member cast, including 13-year-old Isabella Castillo in the title role.
Millions of people around the world have read the journal Anne Frank wrote while she and her family hid from the Nazis in an attic in Amsterdam during World War II.
The Franks were ultimately betrayed and arrested in 1944, with Anne dying in the Bergen-Belsen concentration camp in 1945.
Although the Anne Frank Museum has endorsed the project, Alvero told the BBC not everyone thought the saga would make a good stage musical.
"When I first came here, they had this doubt about how somebody can do a musical of a story like this," he said. "Of course this is emotional. The thing we want to do is through the music, to understand the story better."