Left-back Cummings, 32, was told by manager Neal Ardley that he would not be a regular for the Dons in the forthcoming season.
Ardley told the club's official website: "All the players and staff thoroughly enjoyed working with Warren.
"I know he did have a slow start to last season, but when he did play for me he put in some good performances and he was fantastic around the dressing room.
"That is not always the case when players are out of the team.
"At this stage, with the new signings made, we just felt it was probably best for both parties for Warren to go elsewhere."