Krueger's Oilers went 19-22-7 during his one season.
The 46-year-old Eakins spent the past four seasons with the AHL's Toronto Marlies, reaching the Calder Cup final in 2012.
Eakins was previously an assistant under Paul Maurice with the Maple Leafs for two seasons and was considered an up-and-coming name in NHL coaching circles. He reportedly drew interest from the Dallas Stars and Vancouver Canucks before Monday's hire.
Eakins takes over a young roster that includes No. 1 picks Taylor Hall, Ryan Nugent-Hopkins and Nail Yakupov, along with Jordan Eberle and Justin Schultz.