Peter Jablonski was born in Lyckeby, Sweden to a Polish father and Swedish mother. He studied percussion and piano at Malmö Conservatory from 1982 to 1986. He performed as a drummer at the village vanguard jazz club in New York at the age of nine. He debuted as a pianist in Sweden at the age of 12, with Mozart concerto k 453. In 1989 he moved to the United Kingdom. There he studied composition, conducting and piano at the Royal College of Music in London. He signed to Decca Records in 1991. He made his debuts at Washington's Kennedy Center in 1992 and at London's Royal Festival Hall in 1993. In 2008 he made his conducting debut with the Cracow Philharmonic Orchestra in Sibelius Symphony nr 1.
Washington Post wrote about Jablonski: "It may happen once a season or once in a lifetime. Along comes a talent, not merely your run-of-the-mill virtuoso, but someone, something extraordinary that makes you rethink a piece of music you thought you’ve known forever".
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- Edison Award for recording of the Rhapsody on a theme of Paganini by Rachmaninov with the Royal Philharmonic Orchestra and Vladimir Ashkenazy
- International Swede of the Year 1996
- The 1998 Warsaw Autumn Festival Orpheus Award for his premiere performance of Kilar's Piano Concerto
- The Litteris et Artibus Medal in June 2005 for his achievement as a pianist.