Babers was Eastern Illinois' head coach for two seasons, going 19-7, including 12-2 this season. He guided the Panthers to No. 2 in the final regular-season FCS poll, but Eastern Illinois lost to Towson last week in the FCS quarterfinals.
Under Babers' guidance, quarterback Jimmy Garoppolo passed for 5,050 yards and 53 touchdowns and won the Walter Payton Award as the top player in FCS.
Babers, who will be the first black coach in Bowling Green football history, succeeds Dave Clawson, who took the job at Wake Forest.
Babers was an assistant at Baylor under Art Briles, coaching Robert Griffin III and utilizes an uptempo, spread offense. Babers, 52, has also been an assistant at UCLA, Pittsburgh, Texas A&M and Arizona, San Diego State and Purdue.
The 52-year-old Babers has more than 30 years' experience as an assistant in FBS.
Among other coaches, Bowling Green had also talked to Florida Gators defensive coordinator D.J. Durkin.
The Associated Press contributed to this report.