Johnson replaces Richard Pitino, who was let go last week after eight seasons with the Golden Gophers.
Johnson is a Minneapolis native who graduated from Minnesota in 2005. He played two seasons for the Golden Gophers, averaging around nine points per game, after spending two seasons at Northwestern.
He also spent five seasons as an assistant coach at Minnesota under Pitino, establishing himself as a high-level recruiter in the state. Johnson landed former ESPN 100 recruit and future pro Amir Coffey, among others.
"The University of Minnesota is such a special place and has impacted me in immeasurable ways on and off the court," Johnson said in a statement. "I want to thank President Joan Gabel, [athletic director] Mark Coyle, [deputy AD] Julie Manning and everyone involved in the search process for believing in me and trusting me to lead this historic program. I am ready to get to work."
Per the school, Johnson will receive a five-year contract pending approval from the board of regents.
Johnson has been an assistant under Travis Steele at Xavier for the past three seasons. He also has spent time as an assistant coach at Nebraska and Northern Iowa.
Minnesota has had trouble in recent years keeping top prospects from leaving the state for college, and the Gophers' hope is that Johnson's relationships with the high school and AAU coaches in the area can help keep those players home. He met with Coyle over the weekend and agreed to a deal on Monday.
"Ben is a proven coach who is ready to lead his own program," Coyle said in the statement. "He has earned this opportunity and is a tremendous teacher, recruiter and relationship builder. I am thrilled for him to lead his alma mater, and I am excited for the future of our men's basketball program."