Sólveig studied acting at one of the most respected drama schools in Europe, Ernst Busch in Berlin. She graduated in the year 2000 and has since then worked both in Germany and Iceland.
Sólveig has acted in nearly fifty movies and television plays in Iceland and abroad, besides numerous short films. She has been in more than forty leading roles on stage in Germany and Iceland. She is now under contract at Volksbühne in Berlin, one of the best known theaters in Germany.
Sólveig has won numerous prizes for her acting, both on stage and in films, in Iceland and abroad.