Valverde succeeds Mauricio Pellegrino, who was sacked just hours after the club's 5-2 defeat at home to Real Sociedad on Saturday.
Valverde, 48, has previously coached Athletic Bilbao, Espanyol and Villarreal in Spain as well as two spells with Greek club Olympiakos.
A club statement read: "Valencia have reached an agreement with Ernesto Valverde to be the coach of the first team until June 30, 2013.
"Valverde will be officially unveiled to the media this evening."
Valverde started his coaching career at Athletic, leading the Basque club into the UEFA Cup and the semi-finals of the Copa del Rey.
He then joined Espanyol and guided them to the 2007 UEFA Cup final against Sevilla - a match they lost on a penalty shoot-out at Hampden Park.
He resigned in May 2008 and joined Olympiacos and oversaw a league and cup double in his debut season.
A move to Villarreal came next but he lasted just seven months before being sacked and returning to Olympiacos.
The Piraeus club won the Greek title under his leadership in 2011 and the double once more a year later.
He left Greece for family reasons in April and will now inherit a Valencia squad who feel responsible for Pellegrino's sacking.
Captain Roberto Soldado said: "The coach did his bit in the day-to-day management of the team, but on many occasions those who put in the hours during the week didn't show it in the match.
"The players feel responsible for the current situation.
"We are in no doubt that we, the players, can do the most to turn things around and, in light of the dreadful performance against Real Sociedad, we apologise to all the fans for the ridiculous spectacle we gave.
"It's not up to me to say if the dismissal is fair or not: that's for the board to judge. But the decision has been taken and change is going to come and the players have to knuckle down and get on with it."
Pellegrino left Valencia with the club 11th in the Primera Division standings. Their next game is Wednesday's Champions League clash at Lille. Los Che have already qualified for the knockout phase.