The deal is for four years with a team option for a fifth year. The value of the contract was not immediately disclosed.
McClellin (6-feet-3, 260 pounds) was the No. 19-overall pick in last month's NFL draft. He recorded 20.5 sacks and 33 tackles for loss during his four-year career on Boise State's defensive line.
"There's always pressure that comes with (being a first-round pick), but I'm just going to do what I can; do my job and just get better," McClellin said, according to the Northwest Herald.
Bears coach Lovie Smith praised McClellin after the team's first day of rookie minicamp on Friday.
"He had his hand in the dirt, trying to become a better pass rusher, and that's what it's all about," Smith said.
It previously was reported that McClellin had three concussions in college, although he disputed that, saying he had only one actual concussion.
"I don't know where the reports came from," he said. "I had one concussion in 2010. I didn't miss a game. I missed one practice; they kept me out. In 2009, it wasn't really a concussion. I had concussion-like symptoms, but I was sick before that. It was more precautionary, and it wasn't really a concussion."
Earlier in the day, the Bears agreed to terms with defensive tackles, John McCargo and DeMario Pressley.