"The 25-year-old Croatian international today put pen to paper on a long-term deal with the Reds after completing his medical," the Premier League club's website (www.liverpoolfc.com) said.
Liverpool, runners-up to Manchester City last season and preparing for a return to the Champions League after an absence of nearly five years, have also signed striker Rickie Lambert and midfielder Adam Lallana from Southampton.
"It's a dream come true. I'm happy and glad to be here. I'm proud and can't wait to start. I know we have millions and millions of supporters - Liverpool is more than a club," Lovren, whose career began at Dinamo Zagreb, said.
"After I played at Anfield last season, I said to myself: 'One day I hope I'll be able to play here for Liverpool'. The fans will know from the first minute that I'm a player that will give 100 percent on the pitch."
Lovren was part of the Croatia squad for this year's World Cup finals in Brazil and was unluckily adjudged to have tripped Brazil striker Fred to concede a controversial penalty in the opening match when the score was 1-1.
Croatia eventually lost 3-1 and bowed out in the group stage.
Liverpool have been on a spending spree this off-season after they recouped around 81 million euros ($108.77 million) by selling striker Luis Suarez to Barcelona this month.
They reportedly pulled out of signing France striker Loic Remy from promoted Queens Park Rangers earlier on Sunday after a medical exam.
Lovren made 31 appearances for Southampton since signing from French club Olympique Lyon last year.
(Editing by Greg Stutchbury)
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