Miami gave Arizona a second-round pick in the 2019 NFL Draft and a 2020 fifth round selection for the quarterback. Rosen was the No. 10 overall pick in the 2018 NFL Draft.
Rosen completed 55 percent of his passes and had 11 touchdowns and 14 interceptions during his rookie campaign for the Cardinals. He steps into a Dolphins quarterbacks room that includes veteran Ryan Fitzpatrick. Rosen is expected to compete with Fitzpatrick for the starting job during training camp.
"He's the most talented passer we've had on the roster since Marino," Rubio said. "But he has to be able to play. He's going to get a chance."
Rubio said if the Rosen move doesn't work out, the Dolphins should take another quarterback in the 2020 NFL Draft.
Rosen met with the media for the first time Monday as a member of the Dolphins. He was asked about the Dolphins' search for a franchise quarterback since the end of Marino's decorated career.
"I think I heard I was going to get that question," Rosen said. "But yeah, I'm aware of the situation. Hopefully, I can follow in some semblance of his massive footsteps."