Valverde named new Villarreal coach
Valverde, who led Olympiakos Piraeus to a league and cup double this season, has agreed a one-year contract with an option for a second season, Villarreal said on their website on Tuesday.
Valverde had previous spells in charge of Athletic Bilbao and Espanyol, guiding the latter to the UEFA Cup final in 2007.
Chilean Pellegrini was presented as Real Madrid coach on Tuesday.
Villarreal just missed out on a Champions League place for next season after finishing fifth.