He got his national breakthrough in the 1996 Danish Cup final, when he scored the first goal in the 2–0 win against Brøndby IF.
In February 1999, Degn was bought by English club Everton in the top-flight FA Premier League.
Never a success at Everton, he played four league games as a substitute in his two and a half seasons at the club.
In July 2001, Degn moved back to Denmark, when he signed a four-year contract with Superliga team Brøndby IF.
Having played little more than a year at Vejle, he moved back to the top-flight Superliga in January 2004, when he was bought by Silkeborg IF.