Olsen played 84 matches and scored four goals for the Denmark from 1986 to 1996, and was named 1988 Danish Player of the Year.

Olsen joined Basel's first team for their 1994–95 season under head coach Claude Andrey.

[3] He scored his first goal for the club on 20 November in the away game in the Stadion Allmend against Luzern as Basel won 1–0.

[7] In June 1992, he captained the national team of manager Richard Møller Nielsen in Denmark's first trophy win at the 1992 European Championship.

[7] He re-entered the Danish national team in April 1996 and Olsen was chosen to help Denmark defend the trophy at the 1996 European Championship.

[10] In January 2007, Olsen announced he was moving to become manager of league rivals Odense BK (OB), effective from July 2007.

[10] In September 2010 he and OB sports director Kim Brink were fired due to lacking results.

[12] In November 2011, Olsen moved into international football management by taking over the Faroe Islands becoming the third Dane to do so after Allan Simonsen and Henrik Larsen.

His first victory was against Gibraltar in a friendly match before two UEFA Euro 2016 qualifying wins against Greece.

It was announced that he would remain manager of the Faroe Islands until the end of the UEFA Euro 2020 qualifying in November 2019.