Richards was traded for forwards Brayden Schenn and Wayne Simmonds and a draft choice Thursday. The Kings announced the trade.
Richards had been the Flyers captain and had 23 goals and 66 points this season. He has nine years left on a 12-year contract extension he signed in 2007.
Carter was traded to the Columbus Blue Jackets for forward Jake Voracek and the club's first- and third-round picks.
The Flyers are cleaning house - and cleaning cap room to sign goalie Ilya Bryzgalov. His signing can't be far behind.