Rasmus' older brother Calle and father Peter were both drafted by the New York Rangers, in 2012 and 1983, respectively.

Andersson made his professional debut in his native Sweden, with his local team from youth Malmö Redhawks.

Andersson left Sweden and followed his family footsteps to North America by playing a major junior season with the Barrie Colts of the Ontario Hockey League (OHL) before he was selected by the Calgary Flames in the 2015 NHL Entry Draft.

[2] Andersson began his professional career in North America during the 2016–17 season with the Stockton Heat of the American Hockey League (AHL), recording 22 points in 54 games.

[9] His reassignment to the Heat was short lived, however, as following the Flames season opener, they placed Travis Hamonic on injured reserve and recalled Andersson to the NHL.