The 33-year-old will join the club on July 1 as Mark Warburton's side prepare for their return to the Scottish Premiership.
Barton was named in the Championship team of the year after earning the Clarets automatic promotion to the Premier League, and is moving north of the border for the first time in his coloured career.
Speaking to RangersTV, the former Manchester City, Newcastle and QPR midfielder said: "When I first found out there was potentially the opportunity to come up here, from that moment on the blood got pumping and I thought 'wow, what this could be'.
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"I'm fully aware of the situation the club has been in in the last few years, but to be part of a group that is going to put this football club back where it belongs was an opportunity that if I hadn't taken I would probably have regretted for the rest of my life."
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