The 29-year-old leaves after three years at Goodison Park, during which he made 108 appearances for Everton, scoring four goals.
SSN first reported in January that the French champions were interested in signing the Toffees midfielder.
Everton rejected PSG's initial £21.5m bid despite the player handing in a transfer request.
Everton themselves have signed Fabian Delph from Manchester City and Jonas Lossl from Huddersfield Town so far in the summer window.
While SSN understands, the club are exploring moves for Southampton's Mario Lemina and Chelsea's Fikayo Tomori.
The Toffees view Lemina as a potential replacement for Gueye, with Tomori an alternative option at centre-back if they fail to re-sign Kurt Zouma from Chelsea.
Everton have denied making a second bid for Crystal Palace forward Wilfried Zaha involving cash-plus-players.
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