Grimes started 28 games for the Atlanta Falcons in 2010-11 but was hurt in their opener last year. He declined to predict whether he'll be able to take part in offseason practices beginning in May.
"I don't have any restrictions right now," he said. "I am running and everything. It's just building up your strength and everything. That's part of the process, but I have plenty of time. With the offseason workouts and getting everything in shape, I will be great."
Grimes is expected to start for the Dolphins, who lost Sean Smith via free agency to the Kansas City Chiefs.
"I picked Miami because I think they are building something great here, and I would love to be a part of it," Grimes said.
He was undrafted and broke into the NFL with the Falcons in 2007. He has 13 career interceptions, while Smith has five in four seasons.
"We are very excited that we were able to reach an agreement with Brent," Dolphins general manager Jeff Ireland said. "His experience and history of play making production will add a great deal to our secondary."
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