The score was written by Alan Menkin with lyrics by Glenn Slater, Daily Variety reported Tuesday. The show is aiming for a 2007-2008 season debut.
Among the producers is Michael Manheim, who produced the film and is married to its writer, Variety said.
In the film, Martin played con man Jonas Nightingale who told residents of a drought-stricken rural area that he could make it rain. The stage version will be along the same line, but focus on Nightengale's relationship with a young widow and her son, which eventually brings about his redemption.
Hackford told Variety he has one film project before he devotes all his time to the musical. He has chosen to make his stage debut with "Leap of Faith," even though he was given a similar offer to bring "Ray" to Broadway, Variety said.
"What got me here was Alan Menken's score and how it so beautifully fit the book," Hackford said. "I wasn't interested in doing this with 'Ray,' though I wish them well. I felt that Jamie (Foxx) was my creative partner in that one, and that we said everything we wanted to with the movie."
2014: The Year in Music [PHOTOS]