Lovren has signed a four-year deal and joins for an undisclosed fee.
"I've spoken a lot with the Chairman and the coach, and this is a great project," Lovren said on the club's official website.
"They told me a lot of positive things, and I know the history of the club. It's a big club and I'm very happy that I can be a part of it."
Lovren, who was courted by a number of other European sides, admitted the lure of the Premier League had proved too strong.
"After three and a half years in France, it was a dream to play in the Premier League. Now the dream has come true," he said.
"I have it in my mind to do something big, and I see the same thing in the club.
"We are a young team, and I am a young player also so I hope I will stay here for a long time."