Emery was named new Villa manager on Monday, after the two clubs agreed a compensation fee.
"I enjoyed this journey to the fullest. However, part of the journey is also the ending. And my stage, after the successes achieved, was nearing the end next June. For the past few days, I have been thinking for a long time what my decision might be.
"The farewell is hard and difficult, but my feeling and my reflections tell me to start a new project.
"I will never forget the night in Gdansk, where we touched the sky with a finger. Not even those of Turin, Munich or Bergamo. Or on Sunday, where there was the best tribute to José Manuel (Llaneza). But believe me, the best thing was to come every day to work happy, knowing that you were in a place tailored to you and where you felt respected.
"On that July 27, 2020, during my presentation, I said that my dream was to win a title with Villarreal. Today, after making it, I can tell the fans, the club and my players that I could never have imagined being as happy as I have been with you."