The 48-year-old Spaniard was appointed earlier in the day as a replacement for Mauricio Pellegrino who was sacked on Saturday after a 5-2 home defeat by Real Sociedad left Valencia 12th in La Liga.
"It is the first time I have taken charge of a club mid-season and I consider it a tough task," Valverde told a news conference 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."
Argentine Pellegrino's four-month reign came to an end after Valencia had conceded nine goals in two successive league defeats by Sociedad and Malaga.
"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."
Valencia have qualified for the last 16 of the Champions League and the King's Cup but have been inconsistent in La Liga where they have managed only five wins in 14 outings.
One of Valverde's main tasks will be to stamp his authority on a difficult squad.
A first spell with Olympiakos yielded a league and cup double in 2009 and, after a failed six-month period spent with Villarreal the following year, he returned to Greece to win another league title before last season's repeat double.
