The 24-year-old right-back, who has signed a two-and-a-half-year contract at Ashton Gate, is Sean O'Driscoll's first signing as Robins manager.
"He can play right-back, left-back and centre half and is the right age. He has played a lot of games in the Championship and has never let me down," O'Driscoll told the club's official website.
"Financially, he fits in with what the club want to do in the future and he is reliable and solid as a character.
"He has been at a club where he has not had enough games because they have always had the ability to buy someone more expensive. If they sign someone who is more expensive, they usually play ahead of you."
Moloney made 49 appearances for Nottingham Forest since making his debut in 2007.