The Dutchman joined the Turkish giants from Liverpool earlier this summer, and was quick to advise Meireles to make the move as well, when the Portugal international made contact with him ahead of his transfer.
"Fenerbahce first reached an agreement with Chelsea and only then did I agree personal terms," Meireles stated to Lig TV.
"Maybe people were a bit surprised, but I knew that I joined a very big club. Fenerbahce are the biggest team in Turkey.
"We have a strong squad and are looking forward to playing in the Europa League. Everything is going fine. I'm physically in good shape and ready to play."
The 29-year-old could make his Fenerbahce debut in Sunday's home game versus Mersin Idmanyurdu.