Born in Fredrikstad, Jørn Andersen's career started at local team Østsiden where he remained until 1982. Subsequently, he moved to Fredrikstad and netted seven goals in 43 Norwegian Premier League appearances. The striker was transferred to Vålerenga ahead of the 1985 season. Andersen was able to score 23 goals in just 22 matches for the Oslo side.
Andersen claimed in the Norwegian newspaper Verdens Gang in September 2006 that he had several talks with Joachim Löw to become assistant manager for Germany. The contacts were confirmed by Löw. Andersen says he did not get the position due to his nationality.
In May 2007, he signed to Greek top-flight team Skoda Xanthi to manage them from 2007–08 on, but in June 2007 the contract was dissolved for private reasons.
On 20 May 2008, he signed a two-year deal with 2. Bundesliga outfit FSV Mainz, and under his reign the team achieved promotion to the Bundesliga. Despite the team's success, Andersen was fired on 3 August 2009.
Mid December 2010, he was named manager of the Greek Super League team Larissa. After on 24 days in office, where the team lost three league matches and was knocked out of the cup competition, without scoring a single goal, he was let go.
Six months later, Andersen returned to Germany take charge of second division side Karlsruher SC.