"All the schools that I was interested in, you can't go wrong at any of the programs," Parker said. "It was more of a better, best and best situation I had to chose from."
He later told reporters that his final three included Florida and Michigan State.
Parker is expected to sign a National Letter of Intent in April.
Standing at a podium at Simeon Career Academy in Chicago, the school he has attended for the past seven years, Parker mentioned former college basketball player of the year Jimmer Fredette when he discussed BYU as a final candidate. Baseball caps representing all five schools sat on a table next to the podium.
The Cougars were considered a longshot to land Parker's services, but just making the prep phenom's top five gave coach Dave Rose's program a measure of national notoriety. All four of the other programs favored by Parker have made it to the NCAA Tournament's Final Four in the modern era. BYU has not.
BYU's basketball team and coaches were traveling between Dallas and Waco, Texas, when the announcement was made. The Cougars will play at Baylor on Friday night.
Parker is the cousin of former BYU football star Harvey Unga, the leading rusher in school history. His mother attended BYU, while his father, Sonny Parker, played in the NBA for the Golden State Warriors. His older brother recently returned from an LDS Church mission and is scheduled to enroll at BYU in January.
Thursday's announcement ends a process for BYU coaches that began more than five years ago when they learned of a phenomenal Mormon basketball player from Chicago's south side.
BYU fans sold out the 22,000-seat Marriott Center for a game against Cal State Northridge when Parker visited Provo last month, and fans distributed more than 6,000 T-shirts that read "Chicago to Provo."