Shareef, the eldest son of Hall of Famer Shaquille O'Neal, played sparingly for the Bruins, averaging 2.2 points in 10.2 minutes per game across 13 appearances this season.
He sat out the entire 2018-19 season after the school's medical team discovered an issue with his heart during a routine checkup prior to the campaign.
"After meeting with Shareef on Tuesday, he told me that he plans to transfer," said UCLA head coach Mick Cronin, according to Fox Sports West's Jill Painter Lopez. "We fully support his decision and are wishing him all the best."
Shareef was a four-star recruit coming out of high school, ranking 32nd in the ESPN 100 for 2018.
UCLA is off to a rough start in Cronin's first season, posting a 9-9 overall record, as well as a 2-3 record in Pac-12 play.