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After living in Goodeve, Saskatchewan, and Melville, Saskatchewan, during his childhood, McLellan started his playing career with the Saskatoon Blades of the Western Hockey League (WHL) from 1983 to 1987. In the 1986 NHL Entry Draft, he was drafted by the New York Islanders in the fifth round. He played a total of five games at the NHL level, spending most of two seasons with the Islanders' American Hockey League (AHL) affiliate, the Springfield Indians. However, recurring shoulder injuries dating back to his junior hockey days ended McLellan's North American playing career after the 1988–89 season. He scored his only NHL goal on his league debut on December 28, 1987 in a 6-4 loss to the New Jersey Devils.
Following his stint as a player-coach with SIJ Utrecht, McLellan returned to Canada in 1992. He went into full-time coaching in 1993, being hired as the coach of the North Battleford North Stars of the Saskatchewan Junior League. In 1994, McLellan was hired as the head coach and general manager of the Swift Current Broncos of the WHL, where he succeeded Graham James. In his six seasons with Swift Current, the Broncos qualified for the WHL playoffs in all seasons. McLellan himself was named WHL Executive of the Year in 1997 and Coach of the Year in 2000.
In 1992, McLellan married his wife Debbie. They have two sons, Tyson and Cale.
Following his successes at the junior level, McLellan was hired by the expansion Minnesota Wild to coach their minor league affiliate, the Cleveland Lumberjacks of the International Hockey League (IHL). After the IHL folded in 2001, McLellan and his staff were transferred to the Wild's new minor league affiliate, the Houston Aeros of the AHL. As coach of the Aeros, McLellan led Houston to the Calder Cup in 2003.
In 2005, Mike Babcock selected McLellan to serve as his assistant with the Detroit Red Wings. In Detroit, McLellan was tasked with handling the Red Wings' forwards and managing the team's power play, as well as reporting player performance to head coach Babcock. Under his watch, the Red Wings had the top-ranked power play in the NHL, finishing first in power play efficiency in 2005–06 and third in 2007–08. McLellan won his first Stanley Cup with the Red Wings in 2007–08.
On June 11, 2008, the San Jose Sharks hired McLellan to become their new head coach, replacing Ron Wilson. He would end up the head coach for the Western Conference All-Star team, and lead the Sharks to their first Presidents' Trophy with an NHL-leading 117 points to finish the regular season, and finished third in voting for that season's Jack Adams Award, behind winner Claude Julien and Andy Murray. On March 14, 2013, with a 4–3 victory over the Los Angeles Kings, McLellan became the winningest coach in Sharks history with 207 victories. On February 5, 2014, against the Dallas Stars, McLellan tied Darryl Sutter for the most games coached in Sharks history with 434.
On May 19, 2015, he was named head coach of the Edmonton Oilers, becoming the 14th head coach in team history. He succeeded Todd Nelson, who took over on an interim basis after Dallas Eakins was fired. At the time of his signing, McLellan became the highest paid coach in NHL history, earning around $3 million per season. However, he would hold the distinction for exactly one day, as McLellan's former colleague Mike Babcock signed an eight-year contract with the Toronto Maple Leafs worth around $6.25 million per season on May 20.
McLellan's first season in Edmonton was a rebuilding one. The Oilers finished with 70 points, the second-worst record in the league. However, the following season—the first in the team's new arena, Rogers Place—saw a dramatic turnaround. The Oilers tallied over 100 points for the first time since the 1980s' dynasty years. On March 28, 2017, the Oilers defeated the Los Angeles Kings 2–1 to make the playoffs for the first time in 11 years. They also earned home-ice advantage in a playoff series for the first time since winning their last Cup in 1990. They upended McLellan's old team, the Sharks, in six games to win a playoff series for only the sixth time since 1990.
On November 20, 2018, McLellan was fired by the Oilers and replaced by Ken Hitchcock after posting a record of 9–10–1.
On April 16, 2019, the Los Angeles Kings named McLellan head coach.