Adkins led the Saints to two back to back promotions, taking the South coast club from the lower reaches of League 1 to the Premier League alongside former Iron defender Andy Crosby.
It follows news that Saints' Chairman Nicola Cortese had held talks with Mauricio Pochettino, the former Espanyol boss, about becoming Southampton's next manager.
Pochettino takes over the reigns at St Mary's with immediate effect.
It emerged that Adkins future was still under review by Cortese despite the club's upsurge in fortunes.
The 2-2 draw at Stamford Bridge in midweek saw Southampton up to 15th in the Premier League.
Pochettino was sacked as Espanyol manager in November after the club's poor start to the La Liga campaign. The Barcelona based side were bottom of the league with just nine points from their first 13 games.