Two other Liverpool defenders, Mamadou Sakho and Joe Gomez, are set to miss the start of the season with achilles injuries.
Financial terms of the deal were not disclosed, but British media reports indicated that Klavan had cost Liverpool an initial 4.2 million pounds and had signed a three-year contract.
Klavan is Liverpool manager Juergen Klopp's fifth signing of the close season, following the additions of goalkeeper Loris Karius, central defender Joel Matip, forward Sadio Mane and midfielder Marko Grujic.
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"It's hard to put it into words, because it's been a dream of mine for 22 years to come to the Premier League and be a part of this amazing club, Liverpool," Klavan told Liverpool's website. (www.liverpoolfc.com)
"The Premier League is the most attractive league in the world and you always have amazing players here. This is the home of football."
(Reporting by Simon Jennings in Bengaluru)
