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 Spurs
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, becoming the latest in a long line of Southampton players to leave the club this summer.
Luke Shaw has also exited St Mary's, joining Manchester United, while Morgan Schneiderlin is the subject of interest from Tottenham and Arsenal and Calum Chambers is expected to join the Gunners.