Fells signed as a free agent with Cleveland last season. He made 11 starts and played in all 16 games while helping the Browns finish 7-8-1 after going winless in 2017.
The 32-year-old was used primarily as a blocker and finished with just 11 catches for 117 yards and three touchdowns.
New Browns coach Freddie Kitchens and offensive coordinator Todd Monken want to upgrade tight end and add depth. David Njoku started last season and Seth DeValve is also on the roster but was slowed in 2018 by injuries.
The 6-foot-7, 270-pound Fells played three seasons in Arizona and one with Detroit before signing with the Browns.