Briscoe, a 6-foot-3 New Jersey native who averaged 9.6 points and 5.3 rebounds this past season, made the announcement on his Twitter account.
Briscoe struggled with his perimeter shot as a freshman, making just 5-of-37 shots from beyond the arc. He declared for the NBA draft, but was not invited to the draft combine and decided to withdraw by Wednesday night's deadline to maintain college eligibility.
"I really grew from this experience and I appreciate the opportunity to be evaluated by these NBA teams," Briscoe said in a statement released by the university on Wednesday. "I also want to thank the coaching staff and the fans for their support during this time. The NBA is my ultimate goal, so I'm returning to build on last year. There's no better place to grow as a player or to win a championship, and I want to do both."
Multiple NBA executives told ESPN that Briscoe would have either gone undrafted, or possibly been selected in the latter half of the second round.
"Without his impact and competitive spirit, last year's team would not have been nearly as successful," coach John Calipari said in a statement. "I fully expect him to come back and be a leader on and off the court for this young team. I'm excited to have him back."
Lee, who averaged 6.4 points and 6.0 rebounds along with 59 blocks, told the school that he wants to be closer to his family, Calipari said.
"Marcus Lee informed us today that he is pulling his name out of the draft but has decided he is going to transfer to a school out west to be closer to his family," Calipari said.
"We talked it through together and discussed the team next season, which he said had no bearing on his decision. I also told him he was a semester away from graduating. With that said, he was still adamant that, after the combine experience, a year off and regrouping would be the best thing. As always I support my players and their decisions."
Lee, who ranks 20th all-time at Kentucky with 100 blocked shots, has been granted a full release by the school with no restrictions. Per NCAA transfer rules, he will have to sit out a season.
"I want to thank the University of Kentucky, the basketball staff and the Big Blue Nation for supporting me over the years," said Lee, who is from Antioch, California. "I'm sorry it took me so long to come to this decision, but I'm trying to do what's right for me and my family. I'll always think fondly of my time at Kentucky."
Briscoe's return will give Calipari another talented guard to go along with incoming freshmen De'Aaron Fox and Malik Monk. The Wildcats -- who return Derek Willis, Isaac Humphries and Tai Wynyard up front -- will also bring in freshmen big men Bam Adebayo, Wenyen Gabriel and Sacha Killeya-Jones.