Selected by the Washington Capitals in the first round (No. 23) of the 2006 NHL Draft, Varlamov arrived in North America for the 2008-09 season after four seasons in Russia.

A four-time call-up to the Capitals from the American Hockey League that season, Varlamov was 20 years and 230 days old when he saved 31 of 32 shots to win his NHL debut against the Montreal Canadiens on Dec. 13, 2008. That made him the youngest Russia-born goalie to play in the NHL.

A rookie in 2009-10, Varlamov led Washington in goals-against average (2.55) and shutouts (two), was second in games (26) and wins (15) and finished third among rookie NHL goalies (minimum 26 games) in GAA and save percentage (.909). In 2010-11, he finished tied for fourth in the NHL in GAA (2.23) and had a .924 save percentage, breaking Olie Kolzig's Capitals record of .920 set in 1997-98. But he did not start a game in the 2011 Stanley Cup Playoffs, and on July 1 of that year Washington traded him to the Colorado Avalanche.

Varlamov led the Avalanche in wins the next two seasons. In 2013-14 he benefited from the hiring of Patrick Roy, a former NHL goalie, as Colorado's coach and the installation of Francois Allaire as the goaltending coach. Varlamov finished second in Vezina Trophy voting and fourth in the Hart Trophy balloting after leading the NHL with 41 wins.

He signed a five-year contract with the Avalanche on Jan. 30, 2014.

Varlamov was limited to 24 games during the 2016-17 season because of a hip injury. He went 24-16-6 with a .920 save percentage in 2017-18 was but injured again and did not play in the postseason. He split the goaltending duties with Phillipp Grubauer in 2018-19 and went 20-19-9 with a 2.87 GAA and .909 save percentage in 49 games.

The New York Islanders signed Varlamov to a four-year contract July 1, 2019. He was 19-14-6 with a 2.62 GAA and a .914 save percentage in 45 games when the 2019-20 season was paused March 12 due to concerns surrounding the coronavirus. He played his 500th NHL game Feb. 6, 2021, a 4-3 win against the Pittsburgh Penguins. Two days later, Varlamov became the first Islanders goalie with two shutouts against the New York Rangers after making 30 saves in a 2-0 victory. He shut out the Rangers 3-0 on May 1 to extend his shutout streak to 213:56, passing Chico Resch (178:26) for the longest run without allowing a goal in Islanders history.

Varlamov played his 600th NHL game Feb. 10, 2023, making 19 saves for the Islanders in a 5-2 loss to the Calgary Flames at UBS Arena. He becme the fourth goalie born in Russia to reach the milestone, joining Nikolai Khabibulin, Evgeni Nabokov and Sergei Bobrovsky.

On the international stage, Varlamov represented Russia at the IIHF World Junior Championship in 2006 and 2007.