Bynes, 29, started 11 games for the Cardinals last season before a thumb injury ended his season. He finished with 75 tackles and a career-high two sacks.
The Cardinals will save $1.775 million on their salary cap with the move. He was scheduled to be paid a base salary of $1.5 million in 2019.
Bynes spent his first three seasons with the Baltimore Ravens, who signed him as an undrafted free agent in 2011. He was on the Super Bowl championship team of 2012, and had one tackle in the title game -- on Ted Ginn Jr. after a free kick -- in the final seconds of the game to clinch the Ravens' 34-31 victory over the San Francisco 49ers.
He was signed by the Detroit Lions off the Ravens practice squad on 2014 and played for the Lions for three seasons.
He was signed by the Cardinals to a one-year contract at the league's veteran minimum in 2017, and in March 2018, the Cardinals signed him to a three-year, $5.57 million contract that included $1.25 million guaranteed and a signing bonus of $1 million.