Gad, who stars as Elder Cunningham, announced via twitter that his final performance will be the June 6 free fan appreciation performance at 2 PM.
His co-star Rannells, who plays Elder Price, also revealed via twitter on June 5, "The countdown to my final performance at BOM starts today. I apologize in advance for any over-emotional tweets in the near future." Rannells' final performance will be June 10.
Representatives for The Book of Mormon declined to comment on Gad and Rannells' departure.
The two actors earned Tony nominations for their comedic chemistry as an odd-couple pairing of missionaries – one prays for a sunny assignment in Orlando, while the other's penchant for stretching the truth adds moments from "Star Trek" and "The Lord of the Rings" to the words of Joseph Smith.
Gad will be succeeded by Jared Gertner, who has understudied and performed the role of Cunningham in the Broadway production. Rannells' replacement is Nic Rouleau, who has stoodby for the role of Elder Price since last summer.
The principal cast of The Book of Mormon also features Tony nominee Rory O'Malley (The 25th Annual Putnam County Spelling Bee) as Elder McKinley, Tony winner Nikki M. James (All Shook Up) as Nabulungi and Michael Potts ( Grey Gardens) as Mafala Hatimbi, as well as Lewis Cleale, Scott Barnhardt, Justin Bohon, Darlesia Cearcy, Kevin Duda, Asmeret Ghebremichael, Brian Tyree Henry, Clark Johnsen, John Eric Parker, Jason Michael Snow, Benjamin Schrader, Michael James Scott, Brian Sears, Lawrence Stallings, Maia Nkenge Wilson, Tommar Wilson, Graham Bowen, Tyson Jennette and Nick Spangler.
"South Park" creators-writers Trey Parker and Matt Stone, and Tony-winning Avenue Q songwriter Robert Lopez collaborated on the script and score to the musical, which earned Tony Awards for Best Book, Best Score and Best Musical.