The Red Wings sent minor-league defenseman Sebastien Piche and a first-round pick in this year's draft to the Lightning for the former Detroit draft pick.
Downie, who was drafted in the first round by Philadelphia in 2005, notched 12 goals, 28 points and 121 penalty minutes over 55 games for Tampa Bay this season.
He was coming off a career year in 2010-11, helping the Bolts reach the Eastern Conference finals with 32 points in 57 regular-season games and 14 points in 17 playoff contests.
Quincey's return to the Red Wings comes in his seventh NHL season. He recorded five goals and 23 points in 54 games for the Avalanche this year, his third with Colorado.
He has 16 goals and 92 points over 239 career appearances.