ESPN's Adrian Wojnarowski first reported the hire.
The 41-year-old Gottlieb has led Cal to the NCAA tournament seven times in her eight seasons as head coach, including one Final Four appearance.
Before her hiring at Cal in 2011, Gottlieb spent three seasons as the head coach at UC Santa Barbara, where she won two regular-season Big West Conference titles and reached the NCAA tournament once.
During her 11-year head coaching career, Gottlieb amassed a record of 235-128. That includes a 179-89 mark with the Golden Bears.
Gottlieb played guard at Brown and spent time as an assistant coach at Syracuse, New Hampshire, Richmond and California before going to UC Santa Barbara.
Connor Letourneau of the San Francisco Chronicle believes Gottlieb is a strong hire for the Cavs:
Gottlieb will join a growing number of female assistants in the NBA. Becky Hammon has made the most headlines with the San Antonio Spurs since she is the longest tenured, but Kristi Toliver of the Washington Wizards, Jenny Boucek of the Dallas Mavericks, Natalie Nakase of the Los Angeles Clippers, Karen Stack-Umlauf of the Chicago Bulls and Lindsey Harding of the Philadelphia 76ers are making their presence felt as well.
Beilein and Gottlieb will have their work cut out for them in Cleveland since the Cavaliers went just 19-63 this season following LeBron James' decision to sign with the Los Angeles Lakers.
Despite their struggles, the Cavs have some talent in the form of Kevin Love and Collin Sexton, plus they own the No. 5 overall pick in the 2019 NBA draft, which means Gottlieb should have a strong foundation to help build upon.