He started out in junior hockey with his hometown Port Arthur Flyers in 1944-45 and 1945-46. He then switched to the St Michaels Majors in 1946-47 and won the Memorial Cup. Then in 1947-48 Migay went back home to the Port Arthur West End Bruins. He accomplished the unique feat of winning a second straight Memorial Cup with 2 different teams.
Migay began his National Hockey League career with the Toronto Maple Leafs in 1949. He would play his entire career with the Leafs, leaving the NHL after the 1960 season. The Leafs never traded him as he wished so he never was able to return to the NHL.