He played 18 seasons in the National Hockey League (NHL) for the New Jersey Devils, Hartford Whalers, Carolina Hurricanes, Vancouver Canucks, Philadelphia Flyers, Florida Panthers, Phoenix Coyotes, Tampa Bay Lightning and Los Angeles Kings between 1988 and 2007.

[1] Burke attended St. Michael's college high school and played junior B hockey for the St.Michael's Buzzers in the 1983-84 season.

Instead, he joined coach Dave King and played for the Canadian national team in the Winter Olympics for a second time, backstopping Canada to a silver medal.

On August 28, 1992, Burke was traded to the Hartford Whalers in exchange for Bobby Holík, a second-round pick in the 1993 NHL Entry Draft (used to select Jay Pandolfo) and future considerations.

After that, Burke played for the Philadelphia Flyers (for the second time) recording his 300th career NHL win (the 20th goaltender to reach this milestone), and the Tampa Bay Lightning.

Canada went undefeated in the tournament held in Prague, Czech Republic beating Russia 6 t0 1 in the gold medal game.

In 2017 Burke co managed Team Canada at the IIHF World Championships along with Ron Hextall in Cologne, Germany and Paris, France.

[10] He also spent the 2020-21 season as the full time goaltending coach with the Canadiens as the team made it to the Stanley Cup finals losing to the Tampa Bay Lightning in 5 games.

That same season he co managed the IIHF World Championships with Martin Brodeur and Scott Salmond held in Copenhagen and Herning, Denmark.

[12] Even with the Golden Knights losing their previous season's starting goaltender Robin Lehner for the entire season due to injury and off-season surgery, and rotating through a total of five other goaltenders due to various injuries (by numbers of regular season games started, Logan Thompson, Adin Hill, Laurent Brossoit, Jonathan Quick, and Jiří Patera), Burke was able to help coach the Golden Knights to the Stanley Cup in 2023 (Burke's first Stanley Cup win).

[15] In January 1998, Burke was fined $200, sentenced to 18 months probation, and required to complete an educational program on domestic violence after pleading guilty to the assault charge.