Avery, who is listed at is a 6’1” and 255 pounds, was taken 150th overall.
"I can play inside or outside,” Avery said. “It really doesn't matter. I'm comfortable wherever they want to put me."
In 4 years with the Tigers, Avery played in 50 games – 34 starts – where he totaled 232 tackles, 45.5 tackles for loss, 21.5 sacks, 7 pass breakups and 4 forced fumbles.
Avery will get to join a defense that includes last year’s No. 1 overall pick Myles Garrett, a thought he finds very exciting.
"It feels great. He's a monster,” Avery said. “He's got some much destruction and stuff. I'm so excited to be a part of this organization."
Cleveland has a pair of sixth round selections remaining – Nos. 175 and 188 – Saturday.