Craig MacTavish, the NHL team’s new general manager, made the announcement at a late afternoon presser in the club’s offices.
Strong rumours from multiple sources say Dallas Eakins, currently head coach of the Toronto Marlies in the American Hockey League, is the leading candidate to move behind the Edmonton bench.
Krueger, in his first year, took the Oilers to a disappointing 19-22-7 record in the lockout-shortened 2013 season, missing the playoffs by 10 points.
Born in Winnipeg, Krueger has spent a dozen years as head coach of Switzerland's national team. The 2006 Swiss Olympic team memorably upset Canada 2-0 en route to a sixth-place finish.
They nearly repeated the feat four years later at the Vancouver Games, but Canada prevailed 3-2 in a shootout.
He had been the associate head coach in Edmonton for a year under Tom Renney before getting the main job himself last summer.