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The former Arsenal, Paris Saint-Germain and Sevilla boss has signed a three-year deal with the club, who finished fifth in LaLiga in 2019-2020.
It is Emery's first job since he was sacked by the Gunners last November following a run of just one win in nine games in all competitions.
He succeeded Arsene Wenger at Emirates Stadium in 2018 but failed to secure a return to the Champions League, losing the Europa League final 4-1 to Chelsea last year.
Emery has replaced Javier Calleja, who left Villarreal at the end of the league season despite leading them to a Europa League return.
"I don't t hold any grudge but I'm hurt," he said. "Now it's the turn of Unai Emery and I hope he takes them as high as possible.
"I'm hurt by the way this has happened. I would have done it differently."
Villarreal lost three of its final five games of the season but had previously been on a six-game unbeaten run, which propelled them back into contention for Europe.