Stone is joined by Willie Donachie, who moves up from the club's academy to become development coach while Andy Woodman arrives from Charlton to become the club's new goalkeeping coach.
Peter Beardsley continues as reserve-team manager.
Alan Pardew: "I am delighted to bring Steve, Willie and Alan on board and am sure they will do a tremendous job for the club.
"Keeping Peter with the reserves is important too as he has done a terrific job with the younger lads this season."