Torstensson was born in Nässjö, and studied composition Ingesunds Musikhögskola, musicology at Göteborgs universitet and electronic music at the Institute for Sonology.
Torstensson’s compositions are performed by orchestras, ensembles and soloists worldwide and presented on most major European new music festivals: Huddersfield, Ultima (Oslo), Steirischer Herbst (Graz), Wien Modern, Stockholm New Music, Nordic Music Days (Reykjavik/Malmö/Berlin), Gaudeamus (Amsterdam), Warsaw, Gaida (Vilnius), Festival van Vlaanderen (Belgium), Holland Festival (Amsterdam), GAS (Gothenburg), NYYD (Tallinn) and Darmstadt.
He was also featured composer at festivals such as Stockholm New Music 1999 (together with Mauricio Kagel and György Kurtág), Time of Music 2001, (Viitasaari, Finland), Montréal-Nouvelles-Musiques 2003 and Sacrum Profanum 2009 (Kraków).
During Spring 2009 Klas Torstensson was "composer-in-focus" with the Swedish Radio Symphony Orchestra.
City Imprints, a new composition for large symphony orchestra, was commissioned from Torstensson by the Gothenburg Symphony Orchestra in 2021 to celebrate the city's 400th anniversary.