Toni Martinez and Samir Nasri are also going to depart when their contracts expire at the end of June.
In a statement, joint-chairmen David Sullivan and David Gold said: “Andy and Adrian have both been great servants to West Ham United throughout their time at the club and we thank them for their loyalty and commitment to the claret and blue cause.”
Carroll, 30, joined West Ham from Liverpool in 2012.
He scored the final hat-trick at the Boleyn Ground, against Arsenal and also netted twice against Juventus in the first game at London Stadium.
Meanwhile, goalkeeper Adrian spent five seasons with the Hammers after signing on a free transfer from Real Betis in 2013.
Young midfielders Moses Makasi and Noha Sylvestre and defenders Vashon Neufville and Josh Pask will also depart, as will scholars Mason Barrett, Kevin Dalipi, Jay Mingi, and Odysseas Spyridis.
Tags: Football, West Ham United