Arnesen was capped 52 times and scored 14 goals for the Danish national team, and participated in the Euro 1984 and 1986 FIFA World Cup tournaments.

Arnesen moved from his childhood club Fremad Amager, in the lower leagues of Danish football, to the big Dutch team Ajax in November/December 1975.

In the summer of 1981, Arnesen was bought by the Spanish football club Valencia, and two years later he went to Belgium to play for Anderlecht.

After his active career, Arnesen was first appointed assistant coach at PSV under Bobby Robson from 1991 to 1993, and in 1994 he became the club's general manager.

Arnesen spent ten years as director of football at PSV Eindhoven, and was credited with discovering major talents, such as Brazilian striker Ronaldo and Dutch players Jaap Stam, Ruud van Nistelrooy and Arjen Robben.

Arnesen was photographed aboard one of Roman Abramovich's three luxury yachts on 22 June 2005, thus reinforcing Tottenham's compensation claim.

Arnesen has since played a key role in bringing Salomon Kalou, Florent Malouda and Mikel John Obi to Chelsea.

But the club has still pursued expensive purchases of established international players, rather than unearthing and developing young talent as hoped.

On 27 November 2010, Chelsea announced that Arnesen had resigned as sporting director, and would be leaving the club at the end of the 2010–11 season.