The 30-year-old Estonia defender has signed a three-year contract with the Reds worth an initial £4.2million plus add-ons.
The defender is Jurgen Klopp's fifth signing, following the arrival of goalkeeper Loris Karius, Joel Matip, Marko Grujic and Sadio Mane.
"I'm really honoured to be part of this amazing club, this amazing team," Klavan told the official site.
"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.
"The Premier League is the most attractive league in the world and you always have amazing players here.
"This is the home of football."
He will wear the number 17 shirt.
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