The 6-foot-9, 250-pound All-American power forward is projected to be a top-five pick in the June 26 draft.
"Growing up, I dreamed about playing in the NBA," Randle said. "I came here (Kentucky) to win a national championship, I came here to mature. We came one game short."
Randle, a native of Dallas, Texas, helped lead Kentucky to its 16th Final Four and 12th NCAA title game appearance.
Randle averaged 15.0 points and 10.4 rebounds and was voted to The Associated Press' All-America second team.
Randle is the Wildcats' 12th one-and-done player in five years under coach John Calipari. Teammate James Young became the 11th last week.
Sophomore center Willie Cauley-Stein and freshman forward Marcus Lee both announced they are coming back to school next year. Twin guards Andrew and Aaron Harrison, forward Alex Poythress and center Dakari Johnson have yet to make their intentions known.
Sunday is the deadline for underclassmen to enter the NBA Draft.