"FC Barcelona wants to show its gratitude for the effort and willingness Maxwell has shown since he arrived at the club and for the contribution he made to the sporting successes achieved," Barca said on their website.
The 30-year-old Brazilian joined Barca from Inter Milan at the end of the 2008/09 season and helped them win 10 trophies, including two Spanish leagues titles and one Champions League crown.
He is the latest in a string of signings by ambitious Qatar-backed PSG, who spent around 85 million euros on players in the close season and last month hired Italian coach Carlo Ancelotti.
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