The 24-year-old appeared in the Dolphins' final two preseason games but didn't register a reception.
By signing a reserve/future contract with the Steelers, Griffey will have the chance to impress the coaching staff while on the practice squad.
Breaking through in an offense that includes Antonio Brown, JuJu Smith-Schuster and Martavis Bryant won't be easy, though. Griffey only returned one punt in four seasons with the Arizona Wildcats, so he won't have that to fall back on, either.
Griffey made 79 catches for 1,241 yards and six touchdowns in 35 games for Arizona. Bleacher Report's Matt Miller ranked him as the No. 70 wide receiver in the 2017 draft class.