The 24-year old, who spent three years with the Ligue 1 club since joining from Dinamo Zagreb, attracted interest from a number of European sides, with Liverpool also reported to have been keen on securing his services.
Lovren cost the Saints a fee believed to be in the region of £8million, and he thinks that it is an exciting time to be a part of Mauricio Pochettino's squad.
"I had a discussion with the chairman and the manager, it's a great project and I want to play a part of this project and because of that I want to play here," he told Sky Sports News.
"Now I am here and I am very happy.
"We have a dream and the dream is top seven, top five, top four, I don't know. We want better, of course we want better, and we can do better."