Regin will join the Blackhawks, and Bouchard will report to the Rockford IceHogs of the AHL. The Blackhawks also reassigned forward Brandon Pirri to the IceHogs.
The Islanders will retain 50 percent of Regin's and Bouchard's contracts, a source told ESPN.com's Pierre LeBrun. Both players will be unrestricted free agents after the season.
Regin, 27, has two goals, five assists and a minus-10 rating in 44 games this season. He has played 222 career NHL games over the past six seasons. He had a career-high 13 goals and 26 assists for the Ottawa Senators during the 2009-10 season.
The 29-year-old Bouchard has four goals, five assists and a minus-nine rating in 28 games for the Islanders this season. He also has six goals and 11 assists in 20 games for the Bridgeport Sound Tigers of the AHL this season. He has played 593 career NHL games since 2002.
Pirri was recalled by the Blackhawks on Jan. 27. He had zero points in four games and was a healthy scratch on Wednesday during his stint with the Blackhawks. He has six goals and five assists in 28 games for the Blackhawks this season.