Barton's contract was terminated by the Scottish club on Nov. 10 after a training ground argument with team mate Andy Halliday resulted in a three-week internal suspension.
The outspoken Barton played a key role in Burnley's Championship title success last season, and returns with the club 11th in the top flight on 23 points after 20 matches.
He has been training with Sean Dyche's side since leaving Rangers, but his permanent transfer to the club was in doubt after an FA misconduct charge, with Barton facing a potential fine and suspension following alleged betting offences.
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Before joining Burnley in 2015, the one-time England international had spells with Manchester City, Newcastle United and Queens Park Rangers, while he also spent a season on loan with French giants Olympique de Marseille.
(Reporting by Ed Dove; editing by Ken Ferris)
