League sources told ESPN that Rose has signed for the rest of the 2017-18 season.
"The only thing I'm missing now is the opportunity," Rose told reporters in Minnesota on Thursday. "Talking to Thibs, he sounds like he's going to give me the opportunity, so it's all about learning the guys and fitting in at the right time."
"I think I can play with anybody, to tell you the truth," Rose said. "I know the game. I'm not a selfish player. I'm not here for stats or anything like that. I just want to win and help this team and franchise win."
Rose played sparingly for the Cavaliers this season, leaving the team for two weeks with personal issues. He was the 2011 NBA MVP with the Bulls and a three-time All-Star guard, but several knee injuries have curtailed his dominance.
"We just thought he could help the team," Thibodeau said. "That's what our expectations are: come in, be a good teammate, try to help us win. ... He's been around. He's been in a lot of games. I think he's seen a lot of different things, he's familiar with what we're doing, he's played with some of the guys we have. So that's a plus."
The Associated Press contributed to this report.