The Turkish giants announced the signing of the Holland striker on a three-year contract, ending his six-year spell on Merseyside.
"After six years I am ready for a new challenge," Kuyt said on the website of his management.
"(The club and supporters) I will always carry in my heart.
"The appointment of the new coach has nothing to do with it. But when Fenerbahce came to me and made their ambitions known, from the first moment I was sold. They give me the confidence that I lost."