From 2009 to 2011, Andersen played for the Frederikshavn White Hawks of the Superisligaen, Denmark's top professional ice hockey league.

On 13 March 2010, while playing for the White Hawks, Andersen scored an empty net goal in the fourth quarterfinal match against Rødovre Mighty Bulls.

Taking over with a 3–1 Ducks deficit, he logged two shutout periods, earning him his first NHL win, a 6–3 victory over the Dallas Stars.

On 16 April 2014, Andersen won his Stanley Cup playoff debut as Anaheim defeated the Dallas Stars 4–3 in Game 1 of the Western Conference quarterfinals.

[7] He split time with both Jonas Hiller and John Gibson during the Ducks' run in the 2014 playoffs, which ultimately ended in the Western Conference semifinals against the Los Angeles Kings, the eventual Stanley Cup champions.

The following year, in 2014–15, with Hiller departed via free agency to the Calgary Flames, Andersen and Gibson became the Ducks' goaltending duo.

As the season progressed, however, Andersen assumed the starter's role through both his impressive goaltending play and injuries to Gibson that kept the latter out of the lineup.

He reached the milestone in just 68 career games, tying the record set by the Montreal Canadiens' Bill Durnan on 16 December 1944.

[18] On 3 November, after a 6–3 win against the Chicago Blackhawks, Andersen became the first goaltender in franchise history to go 8–0–0 to start a season with a new team.

Andersen and Ranta received the William M. Jennings Trophy as the goaltenders of the team that allowed the fewest goals during the regular season.

[23] On 6 November 2023, the Hurricanes announced that Andersen would be out indefinitely to address a blood clotting issue that had been discovered during medical testing.

His sister, Amalie, is a defenceman for the Danish women's national team and played in the Premier Hockey Federation (PHF).