Govedaris was born in Toronto, Ontario. As a youth, he played in the 1983 Quebec International Pee-Wee Hockey Tournament with the Toronto Marlboros minor ice hockey team. He was drafted in the first round, 11th overall, by the Hartford Whalers in the 1988 NHL Entry Draft. He played 45 games in the National Hockey League: 33 with the Whalers and 12 with the Toronto Maple Leafs.