Olsen spent his entire football career with his hometown club NSÍ before joining Breiðablik on loan in 2022.

[12] On 13 December 2022, Olsen agreed to join Besta deild karla club Breiðablik on a one-year loan deal.

[13] Olsen was first called up to the Faroe Islands squad in February 2012 for a training camp held in Spain and scored the winning goal in a friendly match against Spanish team La Union.

He made his official debut in a World Cup qualifying match versus Germany on 7 September 2012, coming on as a late substitute.

With 10 goals, he is tied with Rogvi Jacobsen for top scorer in Faroe Islands history.