Björk started his career at IFK Holmsund/Sandviks IK.[3] After spells at Umeå IK and IFK Umeå, he joined Umeå FC at the age of 13 in 2013.[4] Björk made his debut for Umeå FC's first team in the Swedish Division 1 on 10 July 2016 in a 1–1 draw against Nyköpings BIS, where he came on the pitch in the 85th minute.[5]
At the age of 16, he moved from his parents' home in Umeå to Norrköping, where he joined IFK Norrköping in July 2016.[4] He spent the 2017 to 2019 seasons on loan at IF Sylvia. Ahead of the 2019 season, Björk was promoted to IFK Norrköping's first team.[6] Björk made his Allsvenskan debut on 14 June 2020 in a 2–1 win over Kalmar FF.[7]
In August 2020, Björk was loaned out to Trelleborgs FF on a deal for the remainder of the 2020 season.[8] After returning to IFK Norrköping for 2021, he established himself as a key player for the team, scoring eight goals in 27 appearances throughout the season.[3]
On 30 January 2022 it was confirmed that Björk had joined Danish Superliga club Brøndby IF on a deal until June 2026.[9] He made his competitive debut for the club on 20 February, featuring in the starting line-up of a 2–0 league victory against Nordsjælland.[10] He strained his hamstring during the spring, sidelining him for several months.[11]
On 18 August 2023, Björk returned to IFK Norrköping on a one-year loan deal.[12] On 1 July 2024, the clubs agreed to extend the loan agreement, so that it would expire on 31 December 2024.[13][14] He left the club at the end of 2024 when his contract expired.[15]
On February 3, 2025, on the transfer deadline day, it was confirmed that Björk moved to Danish 1st Division club B.93 on a season-long loan deal.[16] After the loan spell, Björk returned to Brøndby in the summer of 2025.[17] However, on 8 July 2025, both clubs confirmed, that Björks loan spell had been extended for the upcoming season.[18]
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