Harris, 28, was released by the Browns earlier this week. A seven-year NFL veteran, he caught 15 passes last season, including three for a touchdown. He has primarily served as a blocking tight end.
Harris spent the first five years of his NFL career with Kansas City, including four years that overlapped with then-Chiefs assistant and current Bears coach Matt Nagy.
The 6-foot-7, 230-pound Harris played college basketball at Wisconsin-Milwaukee. He entered the NFL as an undrafted free agent in 2013.
The Bears haven't confirmed the signing of Harris. The team is free to add him immediately after his release from Cleveland.