The 25-year-old defender arrived at St Mary's for a reported £3.5m fee in January but failed to impress manager Mauricio Pochettino and did not make a first-team appearance last season.
Forren heads back to Norway for an undisclosed fee, but Southampton are understood to have recouped most of the money they paid for his services at the turn of the year.
Midfielder Richard Chaplow has also left St Mary's after his contract was mutually terminated.
The 28-year-old, who was part of the side that secured back-to-back promotions from League One to the top flight, is expected to join Millwall, where he spent part of last season until an injury curtailed his loan spell.
"Southampton football club would like to wish Richard and Vegard the very best in their future careers," the club posted on its official website.
More departures are expected, with Billy Sharp, Dean Hammond, Tadanari Lee, Lee Barnard and Steve de Ridder all told they are free to find new clubs.
Saints have so far only brought in Lyon defender Dejan Lovren, although a move for Celtic's Victor Wanyama is understood to be close to completion.