Minnesota president Gersson Rosas had been trying to move up to No. 4 or 5 before finally getting No. 6, sources said.
Texas Tech shooting guard Jarrett Culver was selected with the No. 6 pick Thursday and will go to the Wolves once the deal is made official on July 6. North Carolina forward Cameron Johnson, who was the No. 11 pick, will go to the Suns.
The Suns had the best chance at the top pick in the draft heading into the lottery before falling to sixth.
Saric averaged 10.5 points and 5.5 rebounds last season, his third in the league and first with Minnesota after being drafted by Philadelphia.
Saric was acquired by Minnesota in the deal that sent Jimmy Butler to Philadelphia. He is under contract next season at $3.5 million, and the Suns will have the right to extend him a $4.8 million qualifying offer for the 2020-21 season. If Phoenix does not, he would become an unrestricted free agent.