The Dutchman has signed a three-year deal believed to be worth around £18m.
Koeman said: “I am very excited to be Everton manager. I believe in the club, in the team, in the fans and in our ability to achieve things in the future.
“Everton is a club with a great history and real ambition and it is a proud feeling for me to be part of what we want to go and do, together with the Chairman and (investor) Farhad Moshiri.
“I am looking forward to meeting everyone at the club and to preparing for a big season in the Premier League.”
Koeman replaces Roberto Martinez, who was sacked by the Toffees before the end of the season.