Everton announced that it is exercising an option to extend Gueye's contract until the summer of 2025.
The club have also offered Seamus Coleman and Ashley Young new one-year contracts.
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Andr Gomes and Andy Lonergan will leave Everton when their contracts expire this summer.
Everton's sporting director Kevin Thelwell said: "Everyone at the club thanks Andr and Andy for their services and contribution to Everton. Andr immersed himself in Everton's values after joining us from Barcelona in 2018 and was, rightly, a popular player with our fans.
"Andy brought vital experience to our talented group of goalkeepers. Both have been valued members of our ranks and we wish them the very best in the future."