The 15-track CD of the show that opened at Broadway's Al Hirschfeld Theatre April 4 will be available May 28, Sony Masterworks label Masterworks Broadway said.
The Broadway cast features Billy Porter, Stark Sands and Annaleigh Ashford, who also appeared in the show in its pre-Broadway Chicago run in October and November.
"Kinky Boots" is based on a 2005 British film of the same name that was inspired by a true story.
The story follows a struggling, family-owned English shoe factory that avoids bankruptcy when its young boss, Charlie (Sands), develops a plan to produce custom fetish-type footwear for drag artists rather than the men's dress shoes his firm was known for.
To save his workers from losing their jobs, Charlie partners with drag queen Lola (Porter) to save the business he inherited.
The Broadway script was written by actor-playwright Harvey Fierstein, who won Tony Awards for writing and originating the lead role in his long-running play "Torch Song Trilogy," about a gay drag performer and his quest for true love and family. Fierstein also wrote the spoken dialogue for the Tony-winning musical "La Cage aux Folles."
Lauper, who is married to "Law & Order" actor David Thornton, is a supporter of lesbian, gay, bisexual and transgender rights, appearing as a grand marshal of New York City's Gay Pride Parade last year.
She has had many hits since she came on the music scene in 1983, including "Girls Just Want to Have Fun," "Time After Time," "True Colors" and "Change of Heart."
Kate Middleton recycles dress at movie premiere
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'