Björk turned professional as a teenager in 2009 and joined the Swedish Golf Tour, where he won his first event as a professional, the Swedish PGA Championship, in his rookie season.
In 2012, Björk became the first golfer to list himself through Trade in Sports, an exchange for athletes, funding the launch of his professional career by pledging 10% of winnings to investors.[3]
In the opening tournament of the 2018 European Tour, Björk shared the lead heading into the final round of UBS Hong Kong Open, but shot his second in the bunker on the final hole and missed a short putt for par and a playoff, finishing tied for second.[8] In April 2018, the week after he finished third at Trophée Hassan II, Björk won his first European Tour title at the Volvo China Open in Beijing, moving into the top ten of the 2018 Race to Dubai rankings[9] and a world ranking of 73.[7] In October he was runner-up at the Sky Sports British Masters. He finished the season 19th in the Race to Dubai and with a career-high world rank of 59.[7]
Björk made less of an impact in 2019 and 2020, but comfortably kept his card. He was tied for third at the Hero Open in England in August 2020, his best finish since 2018.
During 2022, Björk surpassed €5 million in career earnings, but struggled with a back injury and missed the latter part of the season.[10] After three months of rehab, he returned to tour for the 2023 UAE swing, where he finished joint runner-up at the Ras Al Khaimah Championship, one stroke behind Daniel Gavins, missing out on a playoff after a bogey on the final hole.[11]
In September 2023, Björk was solo runner-up at the Omega European Masters, two strokes behind compatriot Ludvig Åberg who birdied four of the closing five holes to record his first win as a professional.[12] He finished the season 11th in the Race to Dubai and 5th in PGA Tour Eligibility Ranking to receive a 2024 PGA Tour card.[13] In his first PGA Tour start, at The American Express, he shot an opening round of 64 to sit 2 strokes off the lead.