The 24-year-old has signed a five-year contract at Anfield and he becomes Jurgen Klopp’s first signing this summer.
Liverpool turned their attention towards Tsimikas after they were priced out of a deal for Norwich City’s Jamal Lewis.
Tsimikas made 27 appearances in the Greek Super League as Olympiacos won the title last season.
"I'm very happy, I'm very proud to be here. For me, [it's] the biggest club in the world," Tsimikas told Liverpool's official website. "It's an honour to be here and I will give my best."
"The league here, I like a lot. I watch it on the TV and it was always one dream I had from when I was a kid to come to play in this league and to come through.
"With a lot of work and focus on what I do and what the coach wants, and every day working hard in training, I can be on the highest level.
"[I want] to achieve [our] goals. To win the league again and also to win the Champions League."
Liverpool manager Klopp added: "We have watched Kostas for a long time and are really happy that he has joined us. It's the perfect news before we come back together very soon.
"He is a very good footballer with an attitude to win and to compete, and I really like his mentality. It fits perfectly with the mood and the desire we have in our dressing room already.
"Kostas knows from personal experience what is required to challenge and succeed domestically and in the Champions League, and he is ambitious for more - just like us."
Tsimikas has won three caps for the Greece national team.
