The 24-year-old striker has spent the past month back with his old club, scoring three times in seven outings in npower League One.
And now the move has been made permanent for an undisclosed fee, Pitman agreeing terms on a three-and-a-half year contract.
Manager Derek McInnes said: "He's gone to a club he knows well and is enjoying regular match action, which is what he wants.
"We wish Brett well for the future."
Pitman moved to Ashton Gate in August 2010 and scored 20 times in 36 starts and 45 substitute appearances but played just four times this season before Eddie Howe moved to bring him back to the south coast until the summer of 2016.