Washington, who is hiring an agent, thanked his Kentucky coaches, teammates and fans for "helping a kid from Dallas see his dreams come true."
The 6-foot-8 Washington averaged 15.2 points and 7.5 rebounds for the Wildcats during the regular season and was a first-team All-SEC selection and third-team All-America.
He missed the first two games of the NCAA tournament with a sprained foot, but returned to score 16 points in a Sweet 16 victory over Houston and had 28 points and 13 rebounds in an overtime loss to Auburn in the Elite Eight.
He is 15th overall in the ESPN 100 rankings for the NBA draft, which will be held June 20.
Washington declared for the draft last year, but he didn't hire an agent and returned to Kentucky in hopes of improving and helping the Wildcats win a national championship.
"I'm so proud of PJ and what he's accomplished over the last two seasons," Kentucky coach John Calipari said in a statement. "When he was in this position last year, he had to determine what was best for him. ...
"What I'm most proud of is how PJ developed into a leader. Every kid is on their own timetable, and the one that PJ followed -- which was the best path for him -- has put him in a position to do some special things at the next level. I can't wait to watch his continued growth."
Also Tuesday, Wildcats guard Ashton Hagans announced via Instagram that he is returning for his sophomore season.
"I had a great meeting with [Hagans]," Calipari wrote on Twitter. "He had a wonderful season but he's not satisfied. He said his desire was to come back and continue to grow and do some special things at Kentucky. That's all I needed to hear. He's ready for the challenge, and I'm all in with him."