The former Rangers midfielder re-joined the club in the January transfer window after a short, yet controversial, stay at Ibrox.
The 34-year-old impressed upon his return, making 14 league appearances as the Clarets successfully staved off relegation from the Premier League.
However, in April he was handed an 18-month ban from football by the English FA for betting on matches.
Barton has appealed the suspension but, with his future up in the air, Burnley have decided not to renew his contract.
He leaves along with winger Michael Kightly.
Manager Sean Dyche said: “Joey leaves us for the obvious reasons after he has again been a big part of what we have achieved this season.
“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.”