Trier averaged 14.8 points this past season and considered testing the waters for the NBA draft. He missed seven games during Pac-12 play because of a right hand injury.
"After talking to Coach [Sean] Miller and my family, I have decided to return to school for my sophomore season," Trier said in a statement. "I am really excited about the quest to become a more complete player. I am also excited to develop as a leader and to lock arms with my teammates while competing for championships. I love being at the University of Arizona and can't wait for next season to begin."
Arizona finished 25-9 this season and lost to Wichita State in the first round of the NCAA tournament.
"I am ecstatic about Allonzo's decision to return to school for his sophomore year,'' Arizona coach Sean Miller said in a statement. "I believe he will become one of college basketball's elite players next season.''
Like talented freshmen Aaron Gordon and Stanley Johnson before him, Trier arrived in the desert loaded with accolades after playing at high school powerhouse Findlay Prep in Las Vegas. The talented 6-foot-6 guard from Seattle lived up to the billing, with a knack for scoring in bunches and the ability to finish at the rim.
Trier's return will give Arizona a potentially dynamic backcourt. Ray Smith was supposed to star alongside Trier this past season, but he missed the season with a torn ACL. He is expected to be back and healthy.
Arizona will add five-star guards Kobi Simmons and Rawle Alkins to the mix, along with Finnish center Lauri Markkanen.
"Allonzo shared his desire to be a leader on a championship team and to improve his overall game,'' Miller said. "By doing so, he puts himself in the best position possible for a very successful NBA future. I have not been around a player that works harder at the game or loves it more than he does. It's this passion to be great that has all of us excited about our future together.''
The Associated Press contributed to this report.