The Chiefs will receive an undisclosed conditional draft pick in the 2018 NFL Draft.
The 6-foot-2, 192-pound Cooper entered the NFL with the San Francisco 49ers as a seventh-round pick out of Rutgers in the 2013 draft. He was waived at the end of training camp by the 49ers and claimed by Kansas City, where he spent the last three seasons.
Cooper appeared in 39 games (11 starts) with the Chiefs, recording 61 tackles, three interceptions, 21 passes defensed, one forced fumble and one fumble recovery.
The 26-year old Cooper saw his most extensive action as a rookie in 2013, when he played in all 16 games (six starts) and had 41 tackles, three interceptions and 18 passes defensed.
The Cardinals have yet to announce their final cuts to get to the 53-man roster by 4 p.m. ET Saturday.