The 27-year-old has left Watford after four years for Goodison Park.
"I have been waiting a long time to come here and now it has happened so I am very happy," Doucoure told the club's website.
"I am so excited to start.
"I feel at the top of my career at the moment. Mentally, physically, I feel at my best.
"I think Everton is the right place now to have a step up and to keep progressing.
"And with the manager and the team we've got, I think I have plenty of time to progress.
"With Mr Ancelotti here it is a good choice for me.
"I am very excited about the project, we are bringing new players like James and Allan.
"Big players. I want to be part of that project.
"I did everything in my power to come here as soon as possible.
"It has been a long time [negotiating the transfer this summer] and I am happy to come here in this exciting moment."
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