The Wolves received the No. 16 overall pick in Thursday night's draft, which was used to select Justin Patton, the freshman center from Creighton.
"What we've done tonight is set a direction," said John Paxson, the Bulls' vice president of basketball operations. "We're going to do it with young players. We're going to be disciplined and patient.
"These are hard things to do. We traded a guy we really like. Tonight, we made a decision to change direction and define our path."
Butler was in Paris when he learned of the trade, according to ESPN's Jeff Goodman. He found out from his agent, Bernie Lee, about 2 a.m. Paris time.
When asked about the deal, Butler told Goodman he did not have a comment.
Dunn was last year's No. 5 overall pick, and LaVine, who averaged 18.9 points last season before suffering a torn ACL, was the No. 13 pick in 2014.
Markkanen, meanwhile, is the first Finnish-born player drafted in the lottery. His 69 3-pointers last season were the most by a 7-footer in college basketball in the past 20 seasons, according to ESPN Stats & Information.
"This is the first opportunity where we felt a deal presented itself that made sense. We got three lottery picks today," Paxson said. "Lauri was the best player on the board. ... He's a guy who fits our team and fits how the game is being played in the NBA."
Following the Butler deal, Minnesota's odds to win the 2017-18 NBA title improved from 100-1 to 60-1 at Westgate Las Vegas. The Bulls went from 100-1 to 200-1.
The trade means a reunion for Butler and Wolves coach Thibodeau, who coached the Bulls for five seasons before being fired in 2015. Butler, 27, played for Thibodeau for four of those seasons. He gives Thibodeau the tough-minded scorer and hard-nosed defender whom he has been searching for to complement a promising young core in Minnesota. Butler averaged 23.9 points, 6.2 rebounds and 5.5 assists last season and has made the all-defensive second team three times.
After Thibodeau joined the Wolves as team president and coach last summer, he quickly set his sights on bringing Butler to Minnesota. The two sides engaged in serious discussions on draft night last year, nearly reaching a deal that would have included LaVine and Dunn -- whom the Bulls were very high on coming out of Providence -- for Butler.
The deal could not be completed, and Butler went through a frustrating season with the Bulls, who brought in Wade and Rajon Rondo in hopes of squeezing some more immediate success out of the group.
"The longer you are with somebody, the more deposits you have with each other, the trust is there," Thibodeau said. "You're not afraid to tell them the truth. So I think I know him well. I know the things that are important to him. I know he wants to win. And he wants to win big.
"The most important thing to me are the things he does every day, the way he practices, the things that he does in meetings, the way he prepares before a game, the things that he does for recovery. He'll show our players a lot of the things that he's learned along the way."
Lee said Butler's appreciation for Thibodeau's hard-driving style increased as time went on, especially when the Bulls struggled in their first season under the more player-friendly Fred Hoiberg.
"They've come by their relationship honestly," Lee said to The Associated Press. "They worked through a period to where they really came to learn what the other is about. ... They have a basis to work from, but things have changed, and they've changed and adapted. They will take the starting point that they have, but they have to build on it."
Thursday's move represents the first significant steps toward an overhaul for the Bulls. Despite a spirited effort, the Bulls were eliminated by the Boston Celtics in the first round of the Eastern Conference playoffs. Wade opted in for the final year of his contract, but that isn't stopping Chicago from pivoting to a new, younger nucleus that includes LaVine, Dunn and Denzel Valentine.
The Bulls said farewell to Butler in a tweet later Thursday.
Meanwhile, one of Butler's trainers, Travelle Gaines, voiced his displeasure with the deal in a tweet, saying the Bulls have "the worst culture in the league."
Butler heads to Minnesota following reports this week that the Cleveland Cavaliers had expressed serious interest in trading for him. Sources told ESPN on Tuesday that the Cavs were notified that Butler preferred to stay with the Bulls and would be reluctant to commit his long-term future to Cleveland.
The Associated Press contributed to this report.