Reed told NFL.com: "The Patriots did come in for me but going in there and trying to learn a new system might have been difficult but once I'd spoken to Rex, I kind of made my mind up.
"The Jets being in the playoff picture was a factor for me, and I know Rex's goals in terms of that. It's awesome to be reunited with him. I know his system and it was a great fit for me and for the team."
Ryan coached Reed when he was a defensive co-ordinator with the Baltimore Ravens, with whom Reed won the Super Bowl back in February.