Sean O'Driscoll confirmed his interest in Moloney earlier this week and the player is set to link up again with the City boss having worked with him at Forest.
Moloney is thought to have agreed a two-and-a-half year deal after passing a medical and holding talks at Ashton Gate.
The versatile defender is understood to have moved on a free transfer due to a release clause in his contract at the City Ground.
The 24-year-old will become O'Driscoll's first signing since he took over at Ashton Gate earlier this month.
Moloney is set to go straight into the squad for Saturday's clash with Ipswich Town