The 29-year-old has spent seven seasons at Upton Park, scoring 59 goals in 237 appearances since joining from London rivals Chelsea.
Cole scored the opening goal in West Ham's Championship play-off final against Blackpool last season, taking his tally for the campaign to 15 as the club earned promotion back to the Premier League at the first time of asking.
Manager Sam Allardyce explained his decision not to retain the man who has won seven caps for England.
"Carlton's need at his age is to be playing football as often as he can," he told the club's official website.
"From our point of view we felt it better that he found pastures new. We can only thank him for his outstanding commitment and service to West Ham United over the last seven years."
Allardyce also confirmed that talks have begun with Gary O'Neil over a new contract for the midfielder.
He added: "For Gary, negotiations are ongoing and that will be done between the chairmen and his agent now."