Reeve Carney, the show's original Peter Parker, played his final performance Sunday night so he can start shooting the new Showtime drama series "Penny Dreadful."
Sargent is best known for his portrayal of bartender-turned-rock-star Drew in Broadway's "Rock of Ages."
"We looked for our new lead in Los Angeles and New York. During Justin's rehearsals as the alternate Peter Parker/Spider-Man, we realized this is the guy to take over for Reeve. He is one of Broadway's great rockers," producers Michael Cohl and Jere Harris said in a joint statement Monday.
The blockbuster musical "Turn Off the Dark" features music and lyrics by Bono and The Edge of U2, and a book co-written by Julie Taymor, Glen Berger and Roberto Aguirre-Sacasa, with direction by Taymor and Philip William McKinley.