For a goalie who was 6-foot-4 and 220 pounds, Andersen somehow flew under the NHL's scouting radar for several years, which is surprising considering he started out playing for Herning, the most successful team in the history of Denmark's top pro league.

In 2008-09, his first season with Herning, Andersen had a goals-against average of 2.45 in 22 games.

However, Andersen was nearly 21 before he was drafted; the Carolina Hurricanes selected him in the seventh round (No. 187) of the 2010 NHL Draft. Realizing the Hurricanes had an entrenched starter in Cam Ward and goaltending depth in their system, Andersen chose not to sign and remained in Europe, playing 2010-11 in Denmark before joining Frolunda of the Swedish Hockey League in 2011-12.

The Anaheim Ducks selected Andersen in the third round (No. 87) of the 2012 NHL Draft, and this time Andersen opted to come to North America. He made his NHL debut Oct. 20, 2013, replacing Jonas Hiller to start the second period in a 6-3 victory against the Dallas Stars. Andersen shut the Stars out in the final two periods, making 24 saves.

After Hiller signed as a free agent with the Calgary Flames on July 1, 2014, Andersen and John Gibson formed a strong goaltending tandem in Anaheim. Andersen, as the No. 1 goalie, went 35-12-5 with a 2.38 GAA and .914 save percentage to help the Ducks advance to the 2015 Western Conference Final.

Andersen earned his 50th NHL victory in his 68th game March 3, 2015, tying Hockey Hall of Famer Bill Durnan's record as the fastest goalie in NHL history to reach the 50-win mark. At that point, Andersen's won-loss record was 50-13-5; Durnan was 50-9 with nine ties.

In 2015-16, Andersen and Gibson won the William M. Jennings Trophy, awarded to the goalies on the team that allows the fewest goals during the regular season (192).

But with Andersen set to become an unrestricted free agent, the Ducks decided they couldn't keep both goalies. On June 20, 2016, they traded Andersen to the Toronto Maple Leafs, who quickly signed him to a five-year contract.

Andersen immediately staked his claim as the No. 1 goalie in Toronto. He started and finished 66 games in each of his first two seasons with the Maple Leafs, winning 33 games in 2016-17 and 38 in 2017-18, helping Toronto make the Stanley Cup Playoffs in back-to-back seasons for the first time since 2002-03 and 2003-04. Andersen continued to be a reliable workhorse. He tied Chris Osgood as the fourth-fastest goalie to reach 200 wins when Toronto defeated the Edmonton Oilers 4-1 on Dec. 14, 2019. Win No. 200 came in his 344th NHL appearance. Andersen also was selected to play in the 2020 NHL All-Star Game.

An unrestricted free agent, Andersen signed a two-year contract with the Hurricanes on July 28, 2021. He teamed with Annti Raanta to win the 2021-22 William M. Jennings Trophy after allowing 202 goals, combining to win the award for the first time in Hurricanes/Hartford Whalers history. 35 games and finishing second in GAA (2.17) and fourth in save percentage (.922). Andersen became the eighth player to win the award with multiple teams (Ed Belfour, Chicago Blackhawks and Dallas Stars; Manny Fernandez, Minnesota Wild and Boston Bruins; Jaroslav Halak, St. Louis Blues and Bruins; Dominik Hasek, Buffalo Sabres and Detroit Red Wings; Robin Lehner, New York Islanders and Vegas Golden Knights; Patrick Roy, Montreal Canadiens and Colorado Avalanche; Roman Turek, Stars and Blues).

Andersen signed a two-year, $6.8 million contract to remain with the Hurricanes on July 1, 2023. He made 22 saves in his 500th NHL game, Carolina's 4-3 victory against the Chicago Blackhawks at United Center on Jan. 20, 2025. Three days later, he earned his 300th NHL win when he defeated the Columbus Blue Jackets 7-4, becoming the second-fastest goalie in NHL history to do so (501 games), trailing only Andrei Vasilevskiy of the Tampa Bay Lightning (490 games).

Andersen signed a one-year, $2.75 million contract with the Hurricanes on May 3, 2025.