The 21-year-old, who was on non-contract terms at non-league St Albans, has impressed manager John Still having spent time training with the Daggers.
Still said: "He is a winger who was recommended to us. We brought him in to have a look at him and he's done very well since arriving so we've signed him up on a long contract.
"He is a young and hungry player who can become another exciting Dagger."
Shields, who plays on the right side of midfield, has not been registered in time to play at Morecambe on Tuesday night.