Galchenyuk played his final year of minor hockey with the U16 Chicago Young Americans and quickly became a star player, tallying 44 goals and 43 assists, leading coach Bruno Bragagnolo to refer to winning a lottery ticket as "the odds of having another kid like Alex play for you". His performance led to him being drafted number one in the 2010 OHL Priority Selection Draft by the Sarnia Sting. Galchenyuk was also selected 25th overall in the 2011 KHL Junior Draft by Atlant Moscow Oblast, which caused his father, Alexander Galchenyuk, to express his displeasure in Alex not being drafted in the first round by the KHL's Belarusian team, Dinamo Minsk. In his first season with the Sting, Galchenyuk recorded 31 goals and 52 assists for 83 total points, which led to him being selected to the OHL 1st All-Rookie team alongside teammate Nail Yakupov. The following year, he missed all but two regular-season games and six playoff games with a knee injury. He was selected third in the 2012 NHL Entry Draft by the Montreal Canadiens. On July 23, 2012, Galchenyuk signed a three-year, entry-level contract with the Canadiens. During the 2012–13 NHL lockout, he played for Sarnia in the OHL, where he served as captain of the team during his final season for the Sting and where he dominated by recording 27 goals and 34 assists in 33 games.
Professional
Montreal Canadiens
Galchenyuk made the Canadiens roster for the 2012–13 season opener, a 2–1 loss to the Toronto Maple Leafs on January 19, 2013. He was the youngest player to play a full season with the Canadiens since 1984. He scored his first NHL goal on January 22, 2013, against Scott Clemmensen of the Florida Panthers, tipping-in a shot from Brandon Prust; rookie teammate Brendan Gallagher also recorded his first NHL point, an assist. Galchenyuk finished the season playing in all 48 games with 9 goals, 18 assists for 27 points and a plus-minus rating of +14, playing primarily on the left wing of the third line. He finished in the top ten in all three offensive categories among rookies, and was sixth overall in rookie points scoring, helping propel a resurgent Canadiens team to the second-best record in the Eastern Conference. During the 2013–14 season, Galchenyuk missed six weeks due to a broken hand. He'd finish the season with 13 goals and 31 points in 65 games. Galchenyuk scored his first career hat-trick on December 16, 2014, against the Carolina Hurricanes. The 2014–15 season also marked Galchenyuk's first 20-goal campaign, as he tallied that amount in 80 games. On July 30, 2015, Galchenyuk signed a two-year, $5.6 million contract extension with the Canadiens. The following season, Galchenyuk tied captain Max Pacioretty with 30 goals to lead the team. Galchenyuk finished second in team scoring with 56 points. On July 5, 2017, Galchenyuk signed a three-year, $14.7 million contract extension with the Canadiens. In the following 2017–18 campaign, Galchenyuk produced 51 points in his sixth season with the Canadiens.
On June 15, 2018, Galchenyuk was traded by the Canadiens to the Arizona Coyotes in exchange for Max Domi. In his first and only season as a member of the Coyotes, Galchenyuk played in 72 games, with 19 goals and 22 assists.
On June 29, 2019, Galchenyuk was traded to the Pittsburgh Penguins along with Pierre-Olivier Joseph in exchange for Phil Kessel, Dane Birks, and a fourth-round pick in 2021. He suffered a lower-body injury early in the 2019–20 season and was placed on injured reserve on October 9, 2019. Galchenyuk returned to make 45 appearances with the Penguins, struggling to match his previous career offensive output in recording 5 goals and 17 points.
Minnesota Wild
On February 10, 2020, Galchenyuk, prospect Calen Addison, and Pittsburgh's first round pick in the 2020 NHL Entry Draft were traded to the Minnesota Wild in exchange for Jason Zucker.
Personal life
Galchenyuk was born in Milwaukee, Wisconsin, to former Soviet and Belarusian hockey player Alexander Galchenyuk and a Belarusian mother. He has an older sister, Anna. Galchenyuk's father was a member of the International Hockey League 's Milwaukee Admirals at the time of his birth. The family moved to Europe when Galchenyuk was four, following his father's hockey career in Germany, Italy and Russia. They eventually settled in Russia, where the younger Galchenyuk began his hockey career before moving back to North America when he was 15, first to Chicago, Illinois, and then to Sarnia, Ontario, where Alex Galchenyuk, Sr. coaches. Galchenyuk serves as the Chairman of Galchenyuk Business Enterprises, GBE, as well as the Galchenyuk Agency. Galchenyuk is an active philanthropist, receiving a Medal of Honor of the National Assembly by the Quebec Government for his efforts in 2015. Galchenyuk speaks three languages: Russian, Italian and English.