Regin played for the Herning Blue Fox of the Danish Elite League from 2002 to 2005, winning Rookie of the Year honors in 2004.

Due to injuries in Ottawa, he was called up and made his NHL debut on 20 January 2009 in a game against the Washington Capitals.

Since beginning his NHL career, Regin has contributed to the rise in popularity of ice hockey in his native Denmark.

[9] During the Blackhawks' training camp, Regin was assigned, along with goaltender Michael Leighton, to their AHL affiliate, the Rockford IceHogs, after clearing waivers.

[13] On 27 April 2021, Regin agreed to a one-year deal with HC Ambrì-Piotta of the National League (NL) for the 2021–22 season.

[14] Regin moved to Germany for the following 2022–23 season, signing a one-year contract with Eisbären Berlin of the Deutsche Eishockey Liga (DEL).