Croatia international Lovren had been linked with a switch to the Premier League runners-up since the end of last season, and made no secret of his desire to leave St Mary's Stadium.
Earlier this month, the 25-year-old told Sportske Novosti in his homeland that his "head is already at Liverpool", while claiming Southampton had rejected a £20 million bid for his services.
However, Lovren has now got his wish after a breakthrough in negotiations between the clubs was apparently made over the weekend and he will join up with Brendan Rodgers' squad on their pre-season tour of the United States.
A statement from the Anfield club on Sunday read: "Liverpool Football Club are delighted to announce the signing of defender Dejan Lovren from Southampton.
"The 25-year-old Croatian international today put pen to paper on a long-term deal with the Reds after completing his medical."
Lovren added: "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."
Lovren joined Southampton from Lyon in June last year, and enjoyed an impressive first campaign in the Premier League.
A regular for his country, the centre-back started all three of Croatia's games at the World Cup in Brazil.
He becomes the third player to make the switch from Southampton to Liverpool this close-season, following Rickie Lambert and Adam Lallana to Merseyside.
