Cunningham's release comes after he was suspended for the Texans' Week 13 loss to the Indianapolis Colts because he was late to his scheduled COVID-19 test.
It marked the second time this season Cunningham did not play for violating team rules. In Week 2 against the Cleveland Browns, he was benched for the first quarter for recurring tardiness.
"We've got standards. Didn't feel like those standards had been met consistently. And I feel like I made a decision that was the best for our team. This is about the team, it's not about any individuals," Culley said.
The coach said the decision to move on from Cunningham "wasn't tough at all."
"It's about the team, it's not about any individual player. And one thing that we always talk about is, it that it's not necessarily trying to being the best player on the team, but being the best player for the team, and that's out motto," he said.
Cunningham, a second-round pick in 2017, signed a four-year, $58 million contract extension in 2020. The linebacker has 67 tackles and one forced fumble this season.
The Texans explored trading Cunningham during training camp and before the trade deadline, but could not find a trade partner.
If Cunningham is claimed, the Texans would save $275,000 (the linebacker's remaining base salary) against the cap in 2021, plus his per game roster bonus. According to OverTheCap, there is a $10 million injury guarantee attached to Cunningham's contract.
The move will leave the Texans with $5.5 million in dead money in 2021 and $12.8 million in 2022 from Cunningham's contract.