Godynyuk played parts of five seasons in the Soviet Union before coming to North America to join the Maple Leaf organization.

He played in 31 more games for the Maple Leafs in the 1991–92 season before being traded to the Calgary Flames in a ten-player deal which brought Doug Gilmour to Toronto.

Godynyuk was selected from the Flames by the Florida Panthers in the 1993 NHL Expansion Draft.

He would move on to the Hartford Whalers midway through the 1993–94 season, and would stay there for the remainder of his NHL career.

The Phoenix Coyotes played their first game in franchise history against the Whalers on October 5, 1996.