Woodall arrived from non-league Gresley last summer on a two-year deal but his impressive contribution during his first season as a professional has earned the 24-year-old a new contract.
Woodall bagged 13 goals in 46 games in all competitions, including a hat-trick on the final day of the campaign, and has subsequently been linked with a move to several Championship clubs, including Nottingham Forest.
Daggers boss John Still told the club's official website: "Brian has signed a new contract and of course we're all delighted, he came here last year from Gresley FC and made a fantastic impression.
"He worked really hard and I'm sure if he keeps working hard then there is a good future for him here and we're all hoping this upcoming season will be a big one for him."
Woodall follows in the footsteps of Daggers duo Dwight Gayle and Billy Bingham, who also signed new deals with the Essex club last week.
