The 27-year-old has joined the Robins after failing to make a Championship appearance for Forest this season.
He will remain at Ashton Gate until January 28 and could make his City debut in Saturday's Sky Bet League One game at home to Oldham.
Gillett's move sees him reunited with City manager Sean O'Driscoll whom he played under at both the City Ground and at previous club Doncaster.
Gillett, who has played two Capital One Cup games for Forest this term, will be playing in the third tier for the first time since 2009 when he was at Southampton.
He had loan spells at Walsall, Blackpool (twice), Bournemouth, Yeovil and Doncaster during his five seasons with Saints.