Regin, 27, tallied two goals and five assists for seven points and 18 penalty minutes in 44 games with the Islanders this season.
The native of Herning, Denmark, has played in 222 career NHL regular-season games with the Ottawa Senators and Islanders and has accumulated 21 goals and 41 assists for 62 points.
He was originally drafted by the Senators in the third-round (87th overall) of the 2004 NHL Entry Draft.
Bouchard, 29, has played in 28 games with the Islanders this season, registering four goals and five assists for nine points.
The native of Sherbrooke, Quebec, has accumulated 110 goals 246 assists for 356 points in 593 career NHL regular-season games with the Minnesota Wild and Islanders.
Bouchard was drafted eighth-overall by the Wild in the 2002 NHL Entry Draft.