The deal is pending league approval Monday.
The Bulls also will ship Lonnie Baxter and Donyell Marshall to the Raptors and get Toronto's Jerome Williams and Chris Jeffries.
"We're giving up talented players," Paxson said, adding that the presence of Davis and Williams will help the Bulls on the inside, where they have young and erratic Eddy Curry and Tyson Chandler.
"This is hard to do, but I think it's right for the organization right now," Paxson said.
Paxson fired coach Bill Cartwright on Monday after Chicago lost 10 of its 14 games, then named Scott Skiles to replace him.
Rose, a small forward in his 10th NBA season, is averaging 13.3 points -- third best on the team -- but he has shot only 38% from the field this season. He would give Toronto, which has struggled to score points, an offensive weapon.
He came to the Bulls in February 2002 in a trade from the Indiana Pacers.
The 6-foot-9 Davis, averaging nine rebounds and 8.6 points, is a veteran presence inside.