Woods, who made one appearance for Leeds last season in a Championship match at the Stadium of Light, said: "Sunderland is a massive club.
"I'm delighted to move here and the set-up is fantastic, it's an exciting move for me. My aim right now is to force my way into first-team set-up."
Woods was offered a new deal by Leeds but told Sunderland's website: "When I learned of Sunderland's interest I was delighted.
"I trained with the lads today and I'm excited about the future."