The fee was agreed between the two clubs on Friday and Lovren has now signed a contract after completing a medical in Liverpool.
Speaking to the club’s official website, Lovren said: "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.
"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."
Liverpool manager Brendan Rodgers added: "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.
"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."
Lovren, who will fly to New York on Monday to join his new team-mates, becomes the most expensive defender in Liverpool’s history with the fee exceeding the £18m the Merseysiders paid Paris Saint-Germain for France international Mamadou Sakho last year.
The former Lyon defender had been linked with a transfer to Anfield throughout the summer, with Rodgers earmarking the 25-year-old as his primary target to reinforce his backline.
Lovren is the third player to trade Southampton for Liverpool this summer, following England duo Rickie Lambert and Adam Lallana in making the switch to Merseyside.
Southampton paid Lyon £8.5m for the Croatia international 13 months ago and he followed up an excellent first season at St Mary’s with some impressive performances during this summer’s World Cup.
Lovren is Liverpool’s fifth signing ahead of the new season so far as Rodgers strengthens his squad ahead of their return to the Champions League.
In addition to Lambert and Lallana, Liverpool have also signed Germany Under-21 midfielder Emre Can from Bayer Leverkusen and Serbia winger Lazar Markovic from Benfica.
Lille’s Belgium striker Divock Origi is also understood to have undergone a medical with Liverpool and is expected to sign for the club imminently.
But one man who won’t be joining Liverpool this summer is QPR striker Loic Remy, after the club pulled the plug on an £8.5m move for the France international.