Anderson, who guided Missouri to a 23-11 record this season before losing to Cincinnati in the second round of the NCAA Tournament, was an assistant coach at Arkansas from 1985-2002.
Before compiling his 111-56 record at Missouri, Anderson was the head coach at Alabama-Birmingham from 2002-06.
"Mike is one of the outstanding head coaches in college basketball," Arkansas Athletics Director Jeff Long said. "His teams play an exciting brand of basketball that has already proven successful at both UAB and Missouri."
Anderson replaces John Pelphrey, who was fired after racking up a 69-59 record during a four-year stay with the Razorbacks.