The offensive tackle, who has not played in the last two games for the Baltimore Ravens, moved to the AFC East side in exchange for a conditional Draft pick.
The 34-year-old told the team's official website: "It feels good to be back here and be able to get a chance to play in front of people who saw me play in college, and to be able to be in my own bed.
"I'm just getting the plays down and everything because today was my first day. To the point where I feel comfortable then I guess it's up to the coach when he feels like I'm ready to go out there.
"I'm getting to know everybody but from the things I've been through I feel like I can contribute as far as experience and help out everybody."
McKinnie has played in 169 NFL games since being drafted in 2002.