The 22-year-old Nordstrom had five goals and three assists in 14 games with Rockford. The forward made his NHL debut with Chicago last season, finishing with a goal and two assists in 16 games, and then made seven more appearances in the playoffs.
The moves were announced on Saturday. The Blackhawks host Dallas on Sunday night.
The 28-year-old Regin had one assist in four games with Chicago after he was recalled from Rockford on Nov. 6.