The percussionist, son of Led Zeppelin legend John Bonham, created the band with the former Deep Purple star, but he is unable to join them on their upcoming dates in the U.S. and Europe due to "professional commitments".
The group has recruited former Queens of the Stone Age drummer Joey Castillo to replace him for the live shows.
A statement posted on the band's Facebook.com page reads, "Glenn Hughes and Andrew Watt have chosen ex Queens of the Stone Age / Eagles Of Death Metal drummer Joey Castillo as the drummer for all upcoming dates when it became clear that Jason Bonham's professional commitments would prevent him from being able to tour with the band."
Hughes adds, "We're just excited to play live, to tour, to be in front of and with our fans. We're very proud of our debut record and we can't wait to share it, live and loud, with you."
The tour kicks off in Detroit, Michigan on 5 October (14).