The group was created in 2004 by Mr. Miranda, Mr. Veneziale and Thomas Kail when they were working on the development of Mr. Miranda’s first Broadway musical, “In the Heights,” which Mr. Kail directed. Mr. Miranda went on to create and star in “Hamilton,” also directed by Mr. Kail; Mr. Veneziale has become an improv educator.

Freestyle Love Supreme has performed periodically around the world, and had a short-lived television show. It had an Off Broadway run earlier this year at the Greenwich House Theater, which is run by Ars Nova, the nonprofit that also housed the first public performances of Freestyle Love Supreme years ago.

“We’re going to try to take all the feeling we captured downtown and put it in the middle of Times Square,” Mr. Kail said in an interview. “It’s a secret more people should know about.”

The Broadway run of “Freestyle Love Supreme” is being produced by Mr. Kail, Mr. Miranda, Jenny and Jon Steingart (founders of Ars Nova), and Jill Furman (a producer of “Hamilton”). It is scheduled to begin performances on Sept. 13 and to open Oct. 2.

The “ Freestyle” run will be one of two on Broadway this season — the other is a one-week run by Dave Chappelle this summer — that will require patrons to secure their smartphones in a locked pouch throughout the performance. The pouches, made by Yondr, are used in other venues, and these shows will be early experiments for Broadway, which has been grappling with how to manage the disruption and distraction caused by cellphones.