Cousins is the second stopper to join the club this summer, as Liam O'Brien also signed for the Daggers.
He told Dagenham's official website: "I've come here to be first team goalkeeper; I think I'm good enough. You've got to have that confidence in the game and I want to."
Dagenham are only Cousins' second club, after a nine-year stay at Colchester and he is ready for a new adventure.
He said: "I'm really pleased, it's a fresh start for me, I've been at Colchester a while. I'm looking forward to the challenge."
He made 70 appearances for the U's and he insists the time was right to leave the Weston Homes Community Stadium.
"It was difficult to leave the people at Colchester but from a footballing point of view it was an easy decision," he added. "I felt I'd been there a long time and wanted a new challenge and new surroundings."