The Texans cut Kalambayi, whom they drafted in the sixth round in 2018, in February.
Kalambayi, 25, played 10 games last season, missing time with a hamstring injury.
He was a core special teams player for the Texans, making 33 tackles in 41 career games over three seasons.
Kalambayi played four seasons at Stanford, totaling 116 solo tackles, 27 tackles for loss, 18.5 sacks, seven pass deflections and an interception.
Cooper has never played an NFL game, but he has spent time with the Falcons and Broncos.