The Islanders had signed each to a one-year contract last summer. Regin had two goals and seven points in 44 games, but had not dressed since last Friday and was scratched for New York's 4-2 loss to the Calgary Flames on Thursday.
Bouchard scored four goals and had nine points in 28 games before being waived. He was playing with the Islanders' American Hockey League team, the Bridgeport Sound Tigers.
Bouchard will report to the Blackhawks' AHL affiliate, the Rockford IceHogs. In addition, forward Brandon Pirri, who has 11 points in 28 games with Chicago this season, was assigned to Rockford.