Lewis will take over the Cardinals' program after the Bruins finish their season. UCLA faces North Carolina in the third round of the NCAA tournament on Friday night.
"We are very excited to return to the state of Indiana where basketball means so much to lead a program with tremendous history and great potential,'' Lewis said in a statement.
He succeeds James Whitford, who was fired March 14 after nine seasons with the Cardinals. Ball State, which hasn't reached an NCAA tournament since 2000, went 14-17 this season, its third losing record in the last four seasons.
"Basketball in our state is personified in Michael Lewis," Ball State athletic director Beth Goetz said in a statement. "His outlook on the game, relationship building, recruiting network, pedigree and proactive approach to engagement with our stakeholders resides at a high level. Additionally, his program values and standards on the court, in the classroom and the community will create a road map for the Cardinals to move onward, compete for Mid-American Conference titles and position our institution for a return to the NCAA Tournament."
Lewis, a standout point guard who still ranks second in career assists at Indiana while playing for coach Bob Knight, has been an assistant coach for 18 seasons, including the past three at UCLA. The Bruins have 68-29 in that span and reached the Final Four last year.
"Michael has the entire package of coaching acumen, player relation skills and recruiting chops to build the Cards into a force in the Mid-American Conference,'' UCLA coach Mick Cronin said in a statement.
A prep star in Indiana, Lewis also was an assistant coach at Butler from 2011 to 2016. The Bulldogs went 108-63 with three NCAA tournament berths during those five seasons.
The Associated Press contributed to this report.