[1] The year following his draft, he was selected to compete for Team Sweden at the 2012 World Junior Ice Hockey Championships.

On 28 May 2013, the Columbus Blue Jackets signed Forsberg to a three-year, entry-level contract,[2] and he was assigned to play with the Springfield Falcons of the American Hockey League (AHL) after the completion of the 2013–14 SHL season.

[3] Forsberg subsequently played his first professional game in North America on 1 April 2014, stopping 25 of 26 shots to lead the Springfield Falcons to a 3–1 win over the Bridgeport Sound Tigers.

[6] In his second season in North America, Forsberg continued playing in the American Hockey League with the Lake Erie Monsters.

[9] After attending the Blue Jackets training camp,[10] Forsberg was reassigned to the American Hockey League to begin the 2016–17 season.

[14] This would be his last season with the Blackhawks as on 24 June 2019, Forsberg was traded to the Carolina Hurricanes along with Gustav Forsling in exchange for Calvin de Haan and Aleksi Saarela.

[16] Prior to the start of the 2020–21 season, Forsberg was waived by the Oilers and subsequently claimed and reacquired by the Carolina Hurricanes on 12 January 2021.

[21] He served as backup to Matt Murray in Ottawa's net, though was initially acquired due to a series of injuries to the goaltenders in the Senators franchise.