McNuff will join former Dons team-mates David Connolly, Nigel Reo-Coker and Adam Nowland at Upton Park.
"He is a great prospect and a confident lad," Hammers boss Alan Pardew told the club's official webiste.
"He was another player that really wanted to come to us, which really appealed to me.
"He has got fantastic speed and unlocks doors, and really causes defences a problem as he travels with the ball quickly.
"I think he he is another player West Ham fans are going to enjoy and we now have three options on the right hand side, when we had none before."