A fee has not been revealed but reports say the deal could be worth around £8 million, with Meireles signing a four-year deal at Sukru Saracoglu Stadium.
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The Portugal international only made the move to Stamford Bridge from Liverpool before the transfer window closed last summer for a fee of £12 million.
Meireles made 42 appearances for The Blues last season and had been involved in every game at the start of this campaign, but was only used as a second half substitute in all three matches.
He has now opted to join fellow former Liverpool team-mate Dirk Kuyt at the Turkish Super League club after failing to establish a regular place in central midfield ahead of preferred partnership John Obi Mikel and Frank Lampard.
Meireles was widely believed to have been unhappy after the club sacked Andre Villas-Boas, the man who brought him to London.
The arrivals of Oscar, Eden Hazard and Marko Marin only further fuelled speculation he could leave the Blues, with new boss Roberto Di Matteo taking on the task of rebuilding Chelsea's squad and bringing in younger talent.
The departures of Yossi Benayoun and Michael Essien on deadline day seemed to have quashed speculation Meireles could leave Stamford Bridge this summer, but it now appears he too was considered surplus to requirements by Di Matteo.