The Reds were being heavily linked with a left-back as they looked for cover for Scottish international Andy Robertson.
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Initially it was reported that they wanted Norwich City's Jamal Lewis but were priced out by the relegated club's demands.
Instead they turn to 24-year-old Tsimikas, who has made three appearances for the Greek national team and was part of the Olympiacos side that won the Greek title this season.
The fee is undisclosed but is reported to be £11.75 million.
“I’m very happy, I’m very proud to be here. For me, [it’s] the biggest club in the world. It’s an honour to be here and I will give my best,” Tsimikas told Liverpool's website.
“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.
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“[I want] to achieve [our] goals. To win the league again and also to win the Champions League.”
Tsimakas will wear No. 21 for Liverpool.
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