Carter cleared waivers Tuesday before the trade was announced.
Carter scored just three points in 18 games this season with the Ducks, struggling to find a consistent role. He has played in 138 games over four seasons with Anaheim.
Chaput and Kennedy both have played for the Hurricanes' AHL affiliate in Charlotte this season. They will join the Ducks' AHL affiliate in Syracuse.
Earlier Tuesday, Anaheim traded defenseman Stu Bickel to the New York Rangers for defenseman Nigel Williams in a swap of minor-leaguers.
New York assigned Bickel to Hartford of the AHL after the deal was completed.
The 24-year-old Bickel has three assists and 14 penalty minutes in six games this season with Syracuse of the AHL. Before joining Syracuse, Bickel played one game with Elmira of the ECHL.
Bickel, 6-foot-4, has played with three teams. He has two goals, six assists and 103 penalty minutes. He was originally signed by Anaheim as a free agent and has never played in an NHL game.
Williams, 22, had one assist in 12 games with Hartford. He was drafted by Colorado in 2006 and traded to the Rangers for Brian Fahey in 2009.