Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
Loan pair Sam Hutchinson and Leon Best have extended their deals at Sheffield Wednesday.
Forren, 24, has signed a three-and-a-half year deal with the Saints.
Capped five times by Norway, Forren was named player of the year in Tippeligaen in November.
Forren, who was at Stamford Bridge on Wednesday to watch Southampton's 2-2 draw with Chelsea, could make his debut against Everton.
Liverpool showed an interest in the defender, inviting him over to England for a trial, but Forren was excited by what the future could hold for Southampton.
"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," Forren said.
"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."