Valverde pleads for patience at Olympiakos
The 46-year-old, who led Olympiakos to a domestic league and cup double in 2009 before a disappointing spell at Spain's Villarreal, has signed a two-year contract and was presented to the Greek media on Tuesday.
Valverde succeeded German coach Ewald Lienen who was sacked after just four games in charge.
"We want to rebuild Olympiakos and make the supporters proud of their team again," said the coach who left under a cloud last year following a fall-out with owner Socrates Kokkalis.
"I had decided to stay in Spain, but eventually chose to come here. I had some personal issues but I couldn't keep saying no to this job," he told a news conference.
"I feel that I have an obligation to the team about how I behaved when I was here. What is needed now, though, is patience and hard work. I know it will not be easy and I don't have a magic wand."
After Valverde's departure in May 2009, Olympiakos went through a succession of coaches including Temuri Ketsbaia, Bozidar Bandovic, Brazilian Zico and Bandovic again before Lienen was appointed two months ago.
They finished fifth following the end of season play-offs and went out of European competition in August for the first time in 19 years with last week's Europa League defeat by Maccabi Tel Aviv.