Söderström joined Brynäs IF as a 14-year old, playing through their junior ranks before he was elevated from the J20 SuperElit and made his professional debut in the Swedish Hockey League (SHL) at the age of 17 during the 2018–19 season on 18 October 2018.

He featured in 35 games from the blueline, reaching new career highs with 5 goals and 16 points in the regular season,[5] before the playoffs were cancelled due to the COVID-19 pandemic.

[6] With the 2020–21 North American season to be delayed, on 1 September 2020, Söderström returned to Sweden in joining second-tier club, AIK of the HockeyAllsvenskan, on loan until the commencement of the Coyotes 2020 training camp.

[9] He also played for Arizona's American Hockey League (AHL) affiliate, the Tucson Roadrunners, scoring two goals and ten points in 32 games.

As a restricted free agent with Utah, Söderström opted to return to Sweden in signing a two-year contract with his original club, Brynäs IF of the SHL, on 15 September 2024.