Cushing has spent nine seasons with the Texans and leaves as the franchise leader in tackles with 664. The move frees $7.64 million of salary cap space in 2018, according to the Houston Chronicle.
The 31-year-old Cushing served a 10-game suspension last season for a violation of the NFL's substance abuse policy. After missing another contest, he returned to start the final four games of the season.
Cushing, who was the 2009 first-round draft pick, was considered expendable because the Texans have second-year linebackers Zach Cunningham and Dylan Cole.
He was named the NFL Defensive Rookie of the Year in 2009 and played in the Pro Bowl in 2010. He has been a starter since he was drafted out of USC.
Knee injuries derailed the 2012 and 2013 seasons, but Cushing came back and missed only five starts because of injuries in the following three seasons.
Cushing has recorded 13.5 sacks, eight interceptions and nine forced fumbles in 104 career games with the Texans.