Koeman claimed he knew was right to swap the south coast for Merseyside after talks with new owner Farhad Moshiri and chairman Bill Kenwright.
The Toffees are preparing for a new era and their new manager will have a huge £100m transfer kitty this summer.
Koeman said: “It was amazing when I had the first contact with the chairman and Farhad Moshiri about their interest.
“I was interested to listen and to hear about their big project, their vision which they want over the coming seasons.
“Of course, I am pleased to be part of that – it’s really enjoyable.”