The No. 3 selection by the Montreal Canadiens in the 2012 NHL Draft, Galchenyuk was born in Milwaukee, where his father, Alexander Galchenyuk, was playing in the American Hockey League. The family would move back to Europe when Alex was 4 and live in Germany, Italy and Russia.
Alexander Galchenyuk, who played internationally for the Soviet Union and Belarus, was serving as an assistant coach with Sarnia of the Ontario Hockey League when Alex began his junior career there. Alex had 31 goals and 83 points in his first season, drawing notice from NHL teams.