The 29-year-old made just one appearance for the Atlanta Falcons in 2012, having sustained a tear to his Achilles tendon in the opening week of the season.
Grimes told the South Florida Sun Sentinel: "They really wanted me here and felt like I could be a big part of what they wanted to do.
"I'm a great playmaker. I play the ball in the air very well. They wanted me here because of my ability to make plays.
"I'm 100% confident that I'll be healthy in no time. Surgeon said six to eight months."
Grimes spent six seasons with the Falcons, making a total of 222 tackles and 13 interceptions.