Columbus Blue Jackets

The next year, still being eligible to play for a junior team, the Columbus Blue Jackets assigned Savard to play with the Springfield Falcons, the team's American Hockey League (AHL) affiliate. After an excellent pro training camp, the Blue Jackets decided Savard would progress faster at the AHL level, following his high marks in junior hockey the former year.^{[citation needed]}

Savard then donned Springfield Falcons colours in the American Hockey League during the 2010–11 season, where he finished as the team's top-scoring defenceman, and second among the league's rookie defencemen.^{[citation needed]}

Savard scored his first career NHL goal on February 7, 2012, against Minnesota Wild goalie Niklas Bäckström. After playing 31 games during the 2011–12 season at the age of 21, he was slowed by an injury suffered in December 2012, shortly before the 2012–13 NHL lock-out's resolution. At the Blue Jackets' camp, he was not able to do justice at the beginning of a season that was going to be shortened, but still managed to be in the lineup for four of the team's 48 games. He spent the majority of the 2012–13 season with Springfield.^{[citation needed]}

On July 15, 2013, as a restricted free agent, Savard was re-signed to a one-year, two-way contract with the Blue Jackets.^[2]

Savard played his first full NHL season with the Blue Jackets during the 2013–14 season, registering 15 points in 70 games. On July 5, 2014, Savard signed a two-year contract with the Blue Jackets.

On September 15, 2015, Savard signed a five-year, $21.25 million contract extension with the Blue Jackets. In the 2016–17 season, Savard led the entire NHL in plus–minus at +33.

Tampa Bay Lightning

Entering the final year of his contract in the pandemic delayed 2020–21 season, Savard, in his tenth season with the Blue Jackets, collected 1 goal and 6 points through 40 regular-season games. Approaching the NHL trade deadline, Savard was involved in a three-way trade, being initially dealt to the Detroit Red Wings with 50% of his salary retained in exchange for Brian Lashoff, before he was flipped to the Tampa Bay Lightning with his salary further retained by the Red Wings in exchange for a 2021 fourth-round pick. The Lightning sent the Blue Jackets a 2021 first-round pick and a 2022 third-round pick in exchange for Lashoff to complete the transaction on April 10, 2021.^[3] He and the Lightning would then go on to win the Stanley Cup, with Savard registering 5 points in 20 playoff games, including an assist on Ross Colton's Cup-clinching goal in game 5.

Montreal Canadiens

After winning the Stanley Cup with the Lightning, Savard would leave in free agency to sign with the Montreal Canadiens on a four-year, $14 million deal on July 28, 2021.^[4] Brought into the lineup at the same time as longtime team captain Shea Weber was placed on long-term injured reserve, Savard was regarded as part of the attempt to compensate for that loss. He became a focus of criticism from fans in the midst of a historically poor season for the team.^[5] On January 29, 2022, it was announced that Savard would miss eight weeks of the season due to an ankle injury.^[6]