The pick is top-14 protected, sources said.
The Jazz needed to make the deal before midnight Friday or they would have lost the $16 million of expiring salary-cap space necessary to pull it off.
Minnesota, meanwhile, cleared space for a big run in free agency after already landing All-Star guard Jimmy Butler in a separate trade earlier in June. The Timberwolves struck quickly by reaching a three-year, $57 million deal with point guard Jeff Teague, sources told ESPN's Adrian Wojnarowski.
"We'd like to thank Ricky for his time in Minnesota over the course of the last six-plus years," Timberwolves coach Tom Thibodeau said. "Ricky has been a consummate professional over my time in Minnesota and has done tremendous things in the community. We appreciate all he's done for the organization and wish him the best of luck in Utah."
Rubio, 26, averaged 16.0 points and 10.5 assists per game after the All-Star break last season.
He posted a thank-you note to Timberwolves fans on Saturday morning, apologizing for not leading the team to the playoffs but saying he wouldn't change his six years in Minnesota.
Basketball brought me here 6 years ago. I didn't know much about Minnesota, and now I'm proud to call it home. You never know what this journey will bring you, and I wouldn't change a bit of mine over the last 6 years. I remember arriving here like it was yesterday. I stepped out of the airport and was overwhelmed with your support. It's something I'll never forget. What we have in Minnesota is special and you don't know that until you live there. You helped me to grow as a player, but more importantly as a person. I learned a lot, met incredible people who became part of my family and will always be in my heart.... especially you, Flip. I gave my best night after night. I'm sorry we couldn't make the playoffs because you deserve it. I am grateful to the Timberwolves organization and all of my coaches, trainers and staff. Finally, I want to thank all of the amazing teammates I was fortunate to play alongside for the last 6 years. I wish nothing but the best for you guys.
Rubio holds career averages of 10.3 points and 8.5 assists but has played 70 or more games just three times in his six NBA seasons because of injuries. His career shooting percentage is .375.
He has two years left on his contract and is owed $14.25 million in 2017-18 and $14.95 million in 2018-19.
The Wolves ended the 2016-17 season with three point guards on the roster. They have now traded two of them (Rubio and Kris Dunn), leaving Tyus Jones as the only player at that position on the roster.
The Knicks had interest in trading for Ricky Rubio but were not willing to part with a first-round pick to obtain the guard, per sources. Minnesota, according to reports, traded Rubio to Utah for a protected first-round pick. GM Steve Mills appears to be following Phil Jackson's rule of valuing first-round picks, which seems wise for a team that appears to be in the midst of a rebuild. On the point guard front, some in the organization like George Hill and Jeff Teague but the Knicks would need to clear cap space to make competitive offers to either guard.
Hill had been with the Jazz, but Rubio's arrival means Hill will land elsewhere in free agency. Hill played a key role in Utah ending a four-year playoff drought despite a variety of injuries that limited him to 49 games last season.
Hill, whose sprained left big toe bothered him for most of the season and ultimately caused him to sit out Utah's final two playoff games, averaged a career-high 16.9 points and 4.2 assists per game while shooting 47.7 percent from the floor and 40.3 percent from 3-point range.
Utah acquired Hill from his hometown Indiana Pacers by dealing the No. 12 overall pick in the 2016 draft in a three-team trade with the Atlanta Hawks, filling the Jazz's glaring need for a starting point guard. The Jazz were 33-16 when Hill played during the regular season and 18-15 when he was sidelined.
The Jazz had interest in signing the 31-year-old Hill to an extension during the season, but he opted to wait to test the open market, confident he would command a significantly larger deal than what Utah offered.
Rubio and Gobert do have a history.
They were on opposite sides of the Spain-France rivalry in EuroBasket during the summer of 2015. Spain defeated France 80-75 in a September 2015 semifinal, and Rubio took exception to Gobert's public dissatisfaction with the officiating after fouling out in overtime.
Gobert, though, indicated Friday that is all in the past.
Let's get it @rickyrubio9 !!!
— Rudy Gobert (@rudygobert27) June 30, 2017
Rubio was drafted by the Timberwolves in 2009 but did not come over from Spain until 2011, electrifying a stagnant franchise with his enthusiasm and no-look passes while also suffering through losing season after losing season. Teaming with Kevin Love, Rubio had the Wolves in position to make the playoffs in the Western Conference as a rookie when he tore the ACL in his knee in a game against the Los Angeles Lakers in March 2012.
Rubio also missed 60 games in 2014-15 with a severely sprained ankle that required surgery. The two major injuries affected his ability to work out during the summer, when players often make the biggest strides in developing their games.
The Associated Press contributed to this report.