The deal also involved draft picks, with the Timberwolves getting two conditional second round choices and the Celtics getting a future first round draft choice.
"We are ecstatic to acquire a player of Wally Szczerbiak's quality," said Danny Ainge, Boston's executive director of basketball operations.
Among the other players in the deal were center Michael Olowokandi, who was a big disappointment with the Timberwolves; and guard Marcus Banks, who had been inconsistent with the Celtics.
Szczerbiak, 28, in his seventh NBA season, is averaging a career-high 20.1 points, 4.8 rebounds and 2.8 assists per game. He was a first round draft pick out of Miami of Ohio in 1999. Davis is averaging 19.7 points, 4.5 rebounds and 5.3 assists per contest.