Valverde guided Valencia to fifth in the league last season before leaving the club.
He replaces Marcelo Bielsa, who after a fantastic first season enjoyed a miserable campaign last time round with the Basque outfit.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.