The 29-year-old has signed a four-year contract with Fenerbahce.
The midfielder joins the Istanbul outfit for a reported fee of £8million.
Meireles joined Chelsea from Premier League rivals Liverpool in 2011, but has fallen down in the pecking order at Stamford Bridge.
Meireles will replace Emre Belozoglu who left Fenerbahce for Atletico Madrid on a free transfer earlier this year.
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Being an amiable guy is good for you and Jurgen Klopp is living proof.
Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.