The Spaniard led the club to their 39th league title this season in his second spell in charge.
"I do not want to dwell too much or become emotional, it's a very difficult day for me," said Valverde whose two-year contract runs out at the end of the season.
"The reasons for my decision are personal. I have completed three years in total with Olympiakos which is a demanding club as the fans always call for victory," Valverde told a news conference.
"In 2008 when I first came to Olympiakos I had no idea what I was getting into. I was surprised with what I saw and was unsure if I had made the right decision. Now I know it was definitely the right decision and I want you to all know that."
Valverde was at the helm when Olympiakos won the title in 2009 and the Basque technician also won the Greek Cup to complete a domestic double in his debut season before a short stint with Villarreal.
He returned to Olympiakos in 2010 to replace Ewald Lienen, helping the club win their 38th league title.
Greek media reports have touted Valencia coach Unai Emery Etxegoien as the prime candidate wanted by Olympiakos owner Vangelis Marinakis to succeed Valverde.
