Emery has been chosen as Steven Gerrard's replacement at Villa Park after a €6m compensation fee exchanged hands between the two clubs.
Emery was in charge of Villarreal for just over two years following a difficult 18-month spell in charge of Arsenal.
The 50-year-old rebuilt his reputation in Spain, leading Villarreal to Europa League glory in 2021 as well as the Champions League semi-finals last season.
Speaking at a farewell press conference on Tuesday, Emery told reporters in an emotional address: "Here I have been very me."
"They gave me the conditions to be my best version of me, [but] you have to continue having challenges.
"In Villarreal I've had a home. I called Fernando [Roig, club president] on Friday to tell him the situation, that I wanted to play the game on Sunday and then on Monday to meet again.
"[On Monday] everything was unleashed. I called Fernando only when there was already something more serious going on."
On his move, Emery added: "It is a professional and personal decision.
"I always carry my baggage, with many complicated and beautiful moments. Here I found a very important family and I have felt something of heart again.
"But the profession is within me. I felt I had to take this option. It's a different challenge, but professionally a very good one."
