Turkish media reports said Meireles had signed a four-year contract. Fenerbahce earlier said they had started negotiations to buy him in a statement to the Istanbul Stock Exchange.
The 29-year-old, who has played more than 60 times for Portugal, was signed by Chelsea on a four-year contract from Premier League rivals Liverpool in 2011.
The Istanbul club, runners-up to Galatasaray last season in Turkey's Super League, have been looking to bolster their midfield after Emre Belozoglu left for Atletico Madrid on a free transfer earlier this year.
Turkey's transfer window closes on Wednesday.
- Istanbul Stock Exchange