Rose said in June that he transferred to his hometown school to be closer to his mother, Marilyn, who is stricken with lupus.
"Family has always been the most important thing to me," Rose said. "With my mother's situation (Houston) was the obvious choice."
Rose was the ninth-ranked point guard in the ESPN100 Class of 2012 and No. 63 overall. He'll be one of four former top-100 recruits in Houston's rotation along with Danuel House, Danrad "Chicken" Knowles and TaShawn Thomas.
Rose originally turned down offers from Arizona, Memphis and Georgetown in favor of Baylor, where he averaged just 0.9 points and 1.2 assists last season as the backup to Big 12 scoring and assists leader Pierre Jackson.
"This past year I learned a lot, especially playing against Pierre every day (in practice)," Rose said. "I matured a lot. I feel like I'm ready to be an impact player."
Rose and his family are certainly familiar with Houston's program. His father lettered for the Cougars' Phi Slama Jama teams from 1980 to '82 and was a sixth-round pick of the Los Angeles Lakers.
He later served on the school's board of regents from 2004 to '09. Rose's uncle, Cecile, scored more than 1,200 points for Houston from 1974 to '78.
Rose spent most of the summer in Houston training under former NBA coach John Lucas.