The 17-year-old has signed a three-year contract with the Toffees.
Everton had an initial bid for the highly-rated youngster rejected earlier this week, but they have now completed the signing of the Scot.
Kennedy made 14 appearances for Kilmarnock since making his debut for the club as a 16-year-old.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.