In a statement on Fenerbahce's website, Cocu said he was "very hopeful" about the vision of the team and its new chairman, businessman Ali Koc.
"I have to say I am very impressed with the club's plans for the near future," Cocu said.
PSV confirmed the move in a separate statement on its own website.
Fenerbahce, under new ownership after two decades, ended the contract of Kocaman after one season on Monday.
Cocu led PSV to their 24th Eredivisie title this past campaign, outlasting rivals Ajax Amsterdam to win their third championship in four years.
(Reporting by Tuvan Gumrukcu; Editing by Christian Radnedge)
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