The 24-year-old, who has signed a three-and-a-half year contract, has five international caps to his name having established himself in the national side last year.
Forren said: "It's a dream come true for me. Southampton is a big club in the Premier League, which is where I have always wanted to come and play football.
"When I was told of the interest from Southampton, straight away I wanted to come and talk to the chairman.
"We had a chat and I was very impressed - there was no doubt that this is where I wanted to be.
"The plan the chairman has for this club is fantastic. There is a good, young squad here and the way they play fits me well, so I hope I can join the team and get some good results."