Högström played in the youth set-ups of Svegs IK, Skellefteå AIK and MODO Hockey.
[1] After two full seasons with Djurgårdens IF in the Elitserie, he left for the Kontinental Hockey League (KHL) in 2016, joining HC Spartak Moscow.
[2] He was waived by the KHL side in late November 2016[3] and accepted an offer from Finnish Liiga outfit HIFK a couple of days later.
[4] During his second stint with Djurgårdens IF, and in the midst of a successful 2017–18 season, Högström was signed to a three-year contract extension through to 2022 on February 7, 2018.
As an impending free agent from the Flames, Högström opted for a return to Sweden in rejoining Djurgårdens IF of the SHL on a two-year contract on May 10, 2019.