"I put a hell of a lot of thought into coming back," Johnson said at his news conference. "For me ... it took a lot of thought, but at the end of the day, you've got to make the right decision. I put a lot of hard thought into it. For me to do what I have to do, I thought this was the best decision."
The 6-foot-7, 245-pound forward averaged 13.8 points and 6.5 rebounds in 28.4 minutes per game for the Wildcats in 2014-15. He was named the Pac-12 Freshman of the Year.
"I have no doubt he'll be a high pick and go on and have a career we'll all be proud of," Miller said of Johnson on Thursday.
Johnson, who does not have an agent yet, is projected to be a lottery pick. ESPN NBA Insider Chad Ford ranks him No. 11 among draft prospects.
Arizona was a No. 2 seed in the NCAA tournament and advanced to the Elite Eight before being knocked out by national runner-up Wisconsin.