Connelly, 27, had five goals, 27 assists and a minus-21 rating for the Iowa Wild of the AHL this season. He has not appeared in an NHL game in his career. He will be an unrestricted free agent after this season.
The Blackhawks said Connelly will report to the Rockford IceHogs of the AHL. He previously played for the IceHogs from 2009 to 2012.
Winchester, 32, had 16 goals, 14 assists and a minus-8 rating in 55 games for the IceHogs. He signed a one-year deal with the Blackhawks as a free agent on July 24, 2013.