He pursued courses at the Royal Academy of Music in Gothenburg (Göteborg), Sweden, training to become a church organist and cantor, but by the time of his graduation in 1978 had shifted to piano, in which he obtained his diploma. He then continued his training with Peter Feuchtwanger in London and Herman D. Koppel in Copenhagen.
He has become known for his wide repertory and his constant interest in finding neglected music. In 1999, he performed Nikolai Medtner’s Second Piano Concerto with the Royal Stockholm Philharmonic Orchestra, played as part of the multi-piano recitals in performances of Stravinsky’s The Wedding and George Antheil’s Ballet mécanique in Copenhagen, and the solo part in Bernstein’s Age of Anxiety Symphony with the Malmö Symphony Orchestra. His repertory includes piano solo works of Erich Wolfgang Korngold, Charles Alkan, Emmanuel Chabrier, and Kaikhosru Sorabji, and his recordings include compositions by Godard, Boëllmann, Koechlin, Pierné, and Alfvén.
Forsberg may be the most esteemed and in-demand accompanists. Among the artists he regularly accompanies are cellist Mats Lidström and violinist Nils-Erik Sparf. With the well-known mezzo-soprano Anne Sofie von Otter he has maintained a long-standing partnership resulting in many recordings on the Deutsche Grammophon label, including a Gramophone ”Record of the Year” Award for 1995 for their program of songs of Edvard Grieg. He and von Otter also collaborated in the BIS label’s ongoing complete Sibelius project. Forsberg also records for Hyperion when partnering with Lidström, and has several releases on the Caprice Records label.
He has a strong interest in French music of the 1800s, and in 1999 began a Saint-Saëns series for Hyperion. He continues to keep a relationship with church music as the director of the chamber music series of the All Saints Church in Stockholm.