The Estonia captain has joined the Reds for a fee of £4.2 million.
He has signed a three-year deal at Anfield and the deal is an initial £4.2m with add ons after the defender completed a medical in Liverpool yesterday.
“I'm really honoured to be part of this amazing club, this amazing team," said Klavan.
“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."