Midfielder Michael Kightly was also released by the club after being loaned out to Championship side Burton Albion in January.
"Joey leaves us for the obvious reasons after he has again been a big part of what we have achieved this season," Burnley manager Sean Dyche told the club's website. (www.burnleyfootballclub.com)
"Equally, 'Kights' has been a great servant of the club and always a tremendous person to have around the group.
"Both players have had a big effect on what we have done during their time at Turf Moor and we wish them well, as we do all those leaving this summer."
Burnley, who Barton helped secure promotion to the top flight in 2016 before he moved to Rangers, finished 16th in the standings to secure a second consecutive season in the Premier League for the first time.
(Reporting by Aditi Prakash in Bengaluru; Editing by John O'Brien)
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