The Nottingham Forest midfielder joined the Robins on loan in November and has made nine appearances - prompting Steve Cotterill to extend his stay with the club.
"We've spoken to Nottingham Forest and they've agreed that we can extend the deal for the rest of the campaign," he told the club's official website.
"Central midfield is where we feel we are a little light and actually somewhere we'd like to strengthen.
"Simon's a great professional and a tidy, intelligent footballer. He reads and understands the game well."
Gillett's current deal doesn't expire until January 28 but the midfielder remains unavailable in the FA Cup and will miss their FA Cup third-round replay with Watford.