Andsnes was born in Karmøy, Norway. He studied with Jiri Hlinka at the Grieg Academy of Music in Bergen.
Andsnes has received numerous awards, including the Hindemith-Prize (1987), Preis der Deutschen Schallplattenkritik (1997), Royal Philharmonic Society Award, (2000), and the Gramophone Awards - Instrumental Award, (2002, for Edvard Grieg's Lyric Pieces).
In 2002 he played Grieg's Piano Concerto at the Last Night of the Proms.
Also a great chamber musician, he holds the position of Artistic Director at the Risør Festival of Chamber Music.