Olsen was born and raised in Copenhagen. She has a degree in musicology and philosophy from the University of Copenhagen and Technische Universität, Berlin. Has worked as music critic at the magazine Dansk Musiktidsskrift and at the two largest daily newspapers in Denmark Berlingske Tidende and Politiken. Has had both weekly and monthly columns at the daily Information.

Olsen made her literary debut in 2000 with Lulus sange og taler (Lulu’s Songs and Speeches) and has since published nine collections of poetry in addition to several dramatic texts and libretti for operas, such as Danish composer Pelle Gudmundsen-Holmgreen’s Sol går op, sol går ned, LEAVES together with Danish indie band Efterklang and composer Karsten Fundal, and composer Peter Bruun’s Miki Alone, which was awarded the Nordic Council Music Prize in 2008.

Olsen has received numerous grants and prizes for her work, including the prestigious award Montanaprisen for Det 3. årtusindes hjerte (Third-Millennium Heart), The Danish Critics’ Award for Udgående fartøj (Outgoing Vessel), and the and the Danish Arts Foundation’s Award of Distinction in 2017. Since November 2018 she is a member of The Danish Academy.

Third-Millennium Heart, her first collection in English, appeared in the US in 2017. Udgående fartøj (Outgoing Vessel) will be published by Action Books in 2020.