Iwar Bergkwist is educated at Teater- och Operahögskolan in Gothenburg. In 1981 he joined Stora Teatern's chorus and became a soloist in 1985. He has sung a number of large tenor parts in both operas and operettas, e.g. Tamino in Die Zauberflöte, Iros in The Return of Odysseus, Pedrillo in Die Entführung aus dem Serail, Count Almaviva in Il Barbiere di Siviglia, Prince Ramiro in La Cenerentola, Fenton in Falstaff, the main role in Werther, Lensky in Eugen Onegin and Boni in The Czardas Princess.
Iwar Bergkwist's roles at the Göteborg Opera include Eisenstein in Die Fledermaus, Narraboth in Salome, which he also sang at the Helsinki Opera, Zefirino in Il Viaggio a Reims, Camille de Rossillon in The Merry Widow, which was also shown on TV, Bob Boles in Peter Grimes and Gaston in La Traviata. During the season 1995-96 he made his debut as a director with the staging of Lars Johan Werle's newly composed opera Äppelkriget at the Göteborg Opera.
In addition to his opera career, Iwar has made several translations and adaptations of musical dramas and also written librettos. He also took a leave of absence from the opera and worked as a teacher, director and principal at Teater- och Operahögskolan in Gothenburg. In the spring 2003 he returned to the Göteborg Opera as Achilles in La Belle Helene, where he was also responsible for the lyrics.
Iwar Bergkwist has performed on several stages outside of Sweden, and is a frequent guest at the Helsingörsteater in Århus.