The deal comes two days after Miami Coach Pat Riley complained about the 6-foot-9 inch Walker being "overweight."
The Timberwolves also got forwards Michael Doleac and Wayne Simien and a future conditional first-round pick.
Riley's move to get Davis is puzzling because they constantly were at odds about Davis' wild, up-and-down playing style and performance when he played for the Heat -- after an ankle injury prevented him from contending for a regular spot in the Heat's 2000-01 season.
The deal comes on the heels of Miami's 0-7 record in the pre-season.
The 6-foot-7 inch Davis, 28, can play big guard and small forward. Last season, he averaged 17 points, 4.8 assists and 3.9 rebounds in 81 games for the Timberwolves.
Walker, 31, an 11-year NBA veteran and three-time All-Star, averaged 8.5 points and 4.3 rebounds in 78 games for Miami.