The former Colorado coach replaces Rob Judson, who was fired earlier this month after his team finished the season with a 7-23 record.
His final season, which began with his announcement that he wouldn't return next year, was his worst. Colorado finished last in the Big 12 for the first time with a 7-20 record and only three conference wins.
The Buffaloes lost to Texas Tech in the opening round of the Big 12 tournament.
The 48-year-old Patton finished his 11-year tenure at Colorado with a 184-160 record, the second-winningest coach in school history.