Left-arm seamer Dwarshuis joins the Phoenix squad with a wealth of experience in T20 cricket around the world, having represented Australia at international level and featured in leading franchise competitions across the globe.
Dwarshuis arrives as a like-for-like replacement for Bangladesh international Rahman, whose unavailability has created an opportunity for one of Australia's most accomplished white-ball bowlers to join the Phoenix setup.
Phoenix Head Coach Shane Bond said: "Ben is a fantastic addition to the squad and someone who brings proven quality, experience and versatility with the ball.
"He's shown his ability to perform in T20 competitions around the world, whether with the new ball or at the death, and we're looking forward to welcoming him to Birmingham Phoenix."
The 32-year-old has built an impressive T20 record across domestic and franchise cricket. His experience in high-profile competitions and international cricket will add further firepower to Birmingham Phoenix's pace-bowling attack, while retaining the left-arm option that Rahman was due to provide.
Everyone at Birmingham Phoenix welcomes Ben to the club and looks forward to seeing him in action in The Hundred.