Kinky Boots will make its world premiere at the Bank of America Theatre in October ahead of a possible Broadway transfer, producers Daryl Roth and Hal Luftig said.
The musical is based on the 2005 British movie about a shoe factory that is struggling following the death of its founder until it finds new life in fetish footwear.
Fierstein, known for his witty musicals like La Cage Aux Folles and Newsies, pushed to have Lauper make her theatrical debut with music and lyrics for Kinky Boots.
"She has one of those big-fat-all-over-the-place-you-can't-hide-it-hearts," he said. "There are just some people that you can't hide it with at all, and she's one of those people."
Lauper, the singer-songwriter behind such hits as True Colours and Girls Just Want to Have Fun, jumped in with a full score that will surprise people, Fierstein said.
"There was a lot of chasing her around because that woman works," he said. "Her musical vocabulary is wonderful. Each character has their own sound."
The musical will be directed and choreographed by Tony winner Jerry Mitchell. Casting and specific dates have not been announced yet.
Fierstein said the story teases out the relationship between Charlie, the shoe factory's new head, and a sassy drag queen performer named Lola.
"It really amplified what, for me, the story was about," he said. "Here are two people who couldn't be more different who realise that, in their minds, they're complete failures to their fathers. They find each other and heal each other."