The 33-year-old is a free agent after helping Burnley win promotion to the Premier League.
Barton tweeted that a “tough decision” has now been made, followed by the words to a well-known Rangers song.
On Tuesday, Burnley announced they had offered a new deal to Barton, as well as former England goalkeeper Paul Robinson.
Goalkeeper Matt Gilks, 33, midfielder Matt Taylor, 34, and winger Lloyd Dyer, 33, have been released by the Clarets.
Long-serving defender Michael Duff, 38, has not been offered a new deal and becomes the under-18s coach.
Championship winners Burnley will also allow goalkeeper Danijel Nizic, 21, and striker Jason Gilchrist, 21, to leave at the end of their contracts in June.
Manager Sean Dyche said: “There are always tough decisions to make at the end of every season – but in football you have to keep moving forwards and on behalf of everyone at the football club, I would like to thank the players leaving us for all their efforts and professionalism.”