The 25-year-old arrives from Leyton Orient, having spent time on loan at Ross County last season.
He made 16 appearances for the Staggies, including the League Cup final victory over Hibernian at Hampden in March.
Woods will provide competition for recent arrival Remi Matthews, who is on a season-long loan at New Douglas Park from Norwich City.
Accies may be in the market for a new central defender after it was revealed Jesus Garcia Tena will miss much of the season with a knee injury.
The 26-year-old was hurt in Hamilton's opening League Cup clash at Ayr United and has now been ruled out for at least six months with ligament damage.
Player-manager Martin Canning is also out injured with a facial injury.
"It is a big blow to lose a player of Jesus' technical ability so early in the season," Canning told the club website. "He is a great reader of the game and his skill set will be a big miss for us."
Hamilton Academical have signed up goalkeeper Gary Woods.