Beginning his playing career with Östers IF and SK Brann, Björklund went on to win three Swedish championships with IFK Göteborg before representing clubs in the Scottish Premiership, Serie A, La Liga, and the Premier League.

Taking the leap from junior team obscurity at Östers IF to becoming a star in Brann, Björklund was later sold to IFK Göteborg.

However the 2003–04 season was better, as he helped Sunderland finish third in Division One and reach the FA Cup semi finals yet his services were deemed to be no longer required by manager Mick McCarthy so he joined Wolverhampton Wanderers, who had just been relegated from the Premier League.

[8] For many years he formed a successful central defensive partnership with Patrik Andersson for the Sweden national team.

Due to lack of playing time at his club Valencia, Björklund was dropped from the Sweden squad during the early stages of the 2002 FIFA World Cup qualifying.

[19][20] On 11 June 2021, Hammarby decided to terminate Stefan Billborn's contract, with the club placed 8th in the 2021 Allsvenskan table after eight rounds, although Björklund stayed in his position for the rest of the year.