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Cole scored in the Championship play-off final that saw the Hammers promoted back to the Premier League, and will depart seven years after joining the club from London rivals Chelsea.
"Carlton's contract has come to an end and we have chosen not to renew that contract," Allardyce told the club's official website.
"At his age Carlton needs to be playing football as often as he can. 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."
Cole, who signed from Chelsea for an undisclosed fee in 2006, has scored 59 goals during his spell with the east London club in 237 games.
Cole has been out of the team for much of the season after the club signed Andy Carroll on loan from Liverpool, and are attempting to make the deal permanent this summer.
Meanwhile, Allardyce announced midfielder Gary O'Neil will be offered a deal. The midfielder signed from Middlesbrough in 2011, and had looked likely to leave the club - but they are now set to keep him.
Allardyce added: "For Gary, negotiations are ongoing and that will be done between the Chairman and his agent now."