Midfielder Chaplow is now free to look for another club, while Forren returns to his native Norway after failing to make a First Team appearance during his six months at Saints.
With first-team opportunities looking slim ahead of the 2013/14 season, Chaplow has been permitted to end his three-year association with Southampton.
The 28-year-old moved to npower Championship side Millwall on loan in March but the switch proved short-lived as an ankle injury forced him to return to Saints having made just four appearances.
The midfielder first joined Saints on loan from West Bromwich Albion in February 2006, scoring once in 11 appearances before heading back to his parent club at the end of the season.
Richard would return to St Mary's more than four years later, again signing on a temporary basis in September 2010 having fallen out of favour at Preston North End.
The move became permanent shortly before the opening of the January transfer window, and Chaplow went on to play a major role in the back-to-back promotions to help Saints return to the top flight.
However, a lack of playing time in the Barclays Premier League saw Chaplow seek regular football elsewhere towards the end of the 2012/13 campaign – a search he will now resume ahead of the upcoming season.
Forren, meanwhile, leaves Southampton for an undisclosed fee having also found opportunities limited in Mauricio Pochettino's First Team since moving from Molde in January.
Vegard made no appearances for the First Team in his short stint with Saints, but was an unused substitute on seven occasions, including for the final away trip of last season at Sunderland.
He maintained his fitness by playing for the Club's Under-21 team, for which he made a total of three appearances, scoring in a 1-1 draw with Liverpool at St Mary's.
With no assurances in place over the regular starting berth Forren is seeking, the 25-year-old now returns to reigning Norwegian champions Molde, the club with which he spent six years before moving to Southampton.
Southampton Football Club would like to wish Richard and Vegard the very best in their future careers.