Fröst was born in Sundsvall, on Sweden's east coast, on December 14, 1970. He began lessons on the violin at age five but switched to the clarinet at eight, studying with Hans Deinzer, Sölve Kingstedt, and Kjell-Inge Stevensson. In the early '90s, he was signed to the BIS label, and he has remained on that label's roster ever since, also making several albums for Sony Classical. Recognition of Fröst's talents was furthered by a first prize at the Geneva Competition in 1997 and a Nippon Music Award the same year for his recording of Carl Nielsen's Clarinet Concerto.
Fröst has appeared with major orchestras in many countries, including the Royal Concertgebouw Orchestra in the Netherlands, the New York Philharmonic, and the Philharmonia Orchestra, among many others, and he plays all of the standard clarinet concerto and chamber repertory. His chamber music collaborators include violinist Janine Jansen and pianists Yuja Wang and Leif Ove Andsnes. An enthusiastic supporter of contemporary music, Fröst has played new works by such major composers as Anders Hillborg, Krzysztof Penderecki, and Kalevi Aho. He was the director of Sweden's Vinterfest Music Festival from 2006 to 2015 and was also joint artistic director of the Stavanger International Chamber Music Festival from 2010 to 2015.
Fröst began his conducting career as conductor-in-association with the Norrköping Symphony Orchestra, and in 2017, he became the principal conductor of the Swedish Chamber Orchestra. He has also developed multimedia projects involving music, choreography, and light design, presenting one about every three years; he appears as a clarinetist, conductor, scriptwriter, and what he calls "master of the ceremony." Fröst has been open about his struggles with Menière's disease. He has continued to perform and conduct, releasing the album Night Passages on Sony Classical in 2022. By that time, his recording catalog comprised more than 20 albums featuring standard repertory, contemporary works, Scandinavian music, and unusual thematic programs featuring music arranged for the clarinet. ~ James Manheim, Rovi