Taking the leap from junior team obscurity to becoming a star in S.K. Brann, he was later sold to IFK Gothenburg. There, his side achieved a surprise 3-1 victory over Manchester United in the group stage of the 1994-95 Champions League. At the end of the following season, he was transferred to Vicenza Calcio and the following year to Rangers, where he won a Scottish league championship medal before moving to Valencia CF in Spain. He spent three years at Valencia before moving to S.S.C. Venezia in Italy, where he was employed for just one season.
Björklund joined Sunderland at the start of the 2002-03 season, but was unable to prevent them from being relegated as statistically the worst Premiership team to date. 2003-04 was better, as he helped Sunderland finish third in Division One and reach the FA Cup semi final. But his services were no longer required by manager Mick McCarthy and he joined Wolverhampton Wanderers, who had just been relegated from the Premiership. He left the club after just one season having failed to get them promoted.
Having finished his playing career, he now works as a scout for Valencia CF. He is mainly scouting the Nordic countries for players.