The centre-back becomes Brendan Rodgers's fifth summer signing and third from Southampton, with Rickie Lambert and Adam Lallana, after rejecting interest from Arsenal and Tottenham
Goal understands the Croatia international has turned down interest from Arsenal and Tottenham to complete the move to Merseyside.
The centre-back was outspoken earlier in July after revealing Southampton had turned down a similar bid without informing him but has now been confirmed as Liverpool's fifth summer signing.
"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," he told the club's official website.
"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 per cent on the pitch."
Lovren joins former Southampton team-mates Rickie Lambert and Adam Lallana at Anfield, and new manager Brendan Rodgers has confirmed the defender will link up with the squad on their US tour.
"This is a very important signing for us and I'm delighted it's completed so Dejan can join up with us on our US tour," Rodgers added.
"He is a commanding and powerful presence and clearly has leadership skills, which is important; he fits the profile of player we are looking for.
"He is still relatively young, so his peak years are ahead of him and I believe he will improve and progress even further with us."
Lovren is the latest name on an ever-expanding list of players leaving Southampton, following Maurico Pochettino - who left for Tottenham - out of the door/
Luke Shaw has joined Manchester United for £30m, while Morgan Schneiderlin is the subject of interest from Tottenham and Arsenal and Calum Chambers is expected to join the Gunners in a £16m deal.