Rabb, a 6-foot-11 power forward, made the announcement during a news conference at his mother's restaurant in Oakland, California.
"I felt the most at home. I felt like it was family from day one," Rabb said during his news conference about his choice. "If anything goes wrong, I'll still have fun there and still enjoy my time on campus.
"This wasn't about staying home. I just felt more comfortable with Coach Martin and the rest of the coaching staff. I was most happy here."
Rabb noted the bond he developed with Martin through the recruiting process was a major factor in his commitment to Cal.
"Our relationship was very important. I got to know him off the court as well. We didn't always talk basketball. We talked about family, life in general."
Kansas, Kentucky and UCLA were also on Rabb's final list, although it was clear over the past couple of months that it was a two-way battle between California and Arizona. The Wildcats seemed like the early favorite due to their connection with the Oakland Soldiers AAU program, but Martin made Rabb his biggest priority since taking over in Berkeley. That relationship between Martin and Rabb ended up winning out.
"They sell me on not just being a part of something, [but] being the start of something," Rabb told ESPN.com at the McDonald's All-American game recently. "It's been a long time since the Bay Area has had a really good program. Coach Martin thinks I can come in and change things around, just change the program. If I went there, I would be the face of the program."
Rabb's commitment helps ease the sting of last week, when top-10 prospect Caleb Swanigan chose Michigan State over California. Swanigan was looked at as a potential starting point to a three-player package deal involving Swanigan, Rabb and No. 2 prospect Jaylen Brown. While that's obviously off the table, Rabb gives Martin an elite-level player to build his program around next season.
About turning his attention to swaying Brown -- the top uncommitted prospect in the class and considering Cal -- Rabb said, "I'm about to step outside and talk to him right now."
Rabb joins four-star small forward Davon Dillard and three-star wing Tyson Jolly in Cal's 2015 recruiting class. Jolly made his decision over the weekend after taking an official visit to Berkeley. Moving forward, Martin will work on several transfer options -- as well as convincing point guard Tyrone Wallace to return for his senior season instead of entering the NBA draft.