Along with the trio of senior players, a host of youngsters will also be released, including Toni Martinez. 13 players in total will depart the club.
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.
Joint-Chairmen David Sullivan and David Gold thanked Carroll and Adrian for their service and wished them and the other departing players all the best for the future.
“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," they said.
“Both have provided us and our fellow supporters with some unforgettable moments, whether they were sensational scissor kicks and unstoppable headers in Andy's case, or penalty saves and goals in Adrian's.
“They can both be assured of warm welcomes whenever they return to London Stadium and we wish them, as well as Samir Nasri and the young players whose contracts are up this summer, the very best for their future careers."