The Warriors also get a 2021 protected first-round draft pick and a 2021 second-round pick and will send Jacob Evans and Omari Spellman to the Timberwolves.
The 2021 pick is top-three protected. If it falls in the top three, it conveys to 2022 and is unprotected.
The Wolves have been looking for a point guard to pair with Karl-Anthony Towns, and they get Russell, who was taken second in the 2015 draft, right behind Towns.
The two are friends, and Towns was on hand to greet Russell when he arrived in Minnesota on Thursday night.
Russell is averaging a career-high 23.6 points per game in his first season in Golden State after he was acquired from Brooklyn in the Kevin Durant deal last July.
Wiggins has spent his entire six-year career in Minnesota. He was the first overall pick of the Cavaliers in 2014 but was part of a blockbuster trade that sentKevin Loveto Cleveland.
Wiggins is averaging 22.4 points and 5.2 rebounds per game.
Russell, 23, has three years left on the $117 million max contract he signed as part of the sign-and-trade between Brooklyn and Golden State.
Wiggins, 24, is in the second year of a five-year,$140 million contract.
Minnesota has been busy leading up to Thursday's NBA trade deadline. The Timberwolves were part of the four-team, 12-player deal that saw them ship Robert Covington to Houston. They received a first-round pick, Atlanta's Evan Turner and Denver's Jarred Vanderbilt,Malik Beasley and Juan Hernangomez.
According to Caesars Sportsbook, the Wolves' chances of winning the NBA title got much better after the Russell trade, but they still don't have much of a chance -- going from 1,000-1 to 250-1.
Wolves make splash with trade for D'Angelo Russell
Brian Windhorst and Paul Pierce react to the Timberwolves acquiring D'Angelo Russell from the Warriors in a deal that includes Andrew Wiggins.
How the Warriors and Wolves pulled off Russell-for-Wiggins deal
Adrian Wojnarowski breaks down the Warriors' trade of D'Angelo Russell to the Timberwolves in a deal that includes Andrew Wiggins.