The 48-year-old Spaniard replaces Pellegrino, who was sacked on Saturday after a 5-2 home defeat to Real Sociedad left the side 12th in La Liga.
Valverde led Olympiakos Piraeus to a Greek league and Cup double last season and has extensive experience in La Liga.
He has worked with Athletic Bilbao and Espanyol, who he guided to the UEFA Cup final in 2007 where they lost to Sevilla.
A first spell with Olympiakos yielded a league and Cup double in 2009 and, after a failed six-month spell with Villarreal in the following year, he returned to Greece to win another league title before last season's repeat double.
His first game at the helm will be in the Champions League away at Lille on Wednesday.
Valencia, who are already qualified for the last 16, have a chance to finish top of Group F ahead of Bayern Munich if they can earn more points than last year's finalists.
"It is the first time I have taken charge of a club mid-season and I consider it a tough task," Valverde said after agreeing a six-month deal.
"When a coach takes over in these circumstances it is because there is a crisis and pressure to get results quickly. The most immediate objective is to transmit my ideas to the team and for the players to gain in confidence."
"I have signed for six months because that is what they offered me," said Valverde. "I hope the team demonstrates enough that I will be able to stay for longer."
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- Real Sociedad