1982 - 1990

    Svif (1982)

    Björn Thoroddsen (1984)

    Plus (1986)

    Quintett (1988)

    Gammar - 1 (1984)

    Gammar - 2 (1985)

    Kuran Swing (1990)   

1991 - 2000

    Gammar - Af Niðafjöllum (1992)

    Við Göngum svo Léttir (1993)

    Híf opp (1996)

    BT Jazz Guitar (1997)

    Hvar Sem Sólin Skín (1999)

    Guitar Islancio (1999)

    Kuran Swing - Music to my Ears (2000)

    Guitar Islancio II (2000)

2001 - 2010

    Guitar Islancio III (2001)

    Jazz í Reykjavík (2002)

    Guitar Islancio - Connections (2002)

    Jazz Airs - Svare/Thoroddsen (2003)

    Luther (2004)

    Cold Front  – X-mas (2005)

    Sweet and Lovely - Svare/Thoroddsen (2005)

    Trio BT & Kristjana - Jól (2005)

    Guitar Islancio - Icelandic Folk (2005)

    Trio BT & Andrea - Vorvindar (2006)

    Trio BT & Andrea - Vorvísur (2007)

    Cold Front - Full House (2007)

    Trio BT & Andrea - Í Heiðanna ró (2009)

2011 -

    Fúsi Halldórs Vinsælustu lögin (2010)

    Björn Thoroddsen & Richard Gillis - Rhymes (2010)

    Björn Thoroddsen & Richard Gillis - Morgana's Revenge (2011)

    Björn Thoroddsen & Richard Gillis - The Journey (2013)

    Björn Thoroddsen plays The Beatles (2013)

     Bjössi featuring Mackenzie Wasner (2017)

    Svif (Digital reissue of 1982 album) (2017)