Barbara Pasternack, a theater producer, remembered waiting for a train to the Hamptons in 2007 when she stepped into a bookstore at Penn Station and picked up “The Lightning Thief,” the best-selling young adult novel by Rick Riordan.

By the time she arrived at her destination, she had finished the 300-plus page book about Percy Jackson, a 12-year-old boy who discovers he is the son of Poseidon, the Greek god of the sea.

“I fell into it,” said Ms. Pasternack, the artistic director of TheaterworksUSA, which produces shows for young adults and families. She was not alone. Mr. Riordan’s Percy Jackson books have been New York Times best sellers.

Now, 12 years, an original rock score and a 32-city North American tour later, “The Lightning Thief: The Percy Jackson Musical,” is coming to Broadway. The show is scheduled to begin performances Sept. 20 at the Longacre Theater for an Oct. 16 opening. A limited run, it will close Jan. 5, 2020.