The Saints are 15th in the Barclays Premier League after coming back from 2-0 down to claim a draw with European champions Chelsea at Stamford Bridge on Wednesday.
But that was not enough to save Adkins from the axe, with 40-year-old Argentinian Pochettino taking charge of training on Saturday ahead of Monday's home game with Everton.
Pochettino, the former Argentina international, will take charge of Southampton for Monday's game against Everton.
Saints executive chairman Nicola Cortese said: "This decision has been made with the long-term ambitions of Southampton Football Club in mind.
"Whilst we acknowledge the contribution Nigel has made during the past two years, for the club to progress and achieve our long-term targets a change was needed.
"Mauricio is a well-respected coach of substantial quality who has gained a reputation as an astute tactician and excellent man-manager. I have every confidence that he will inspire our talented squad of players to perform at the highest possible level.
"He also shares my belief that the most successful clubs are built by nurturing young players through a development system that provides a clear path to the first team, thereby creating a culture that keeps them at the club for the long term.
"This is an approach he has employed with great success in the past and I look forward to him bringing that experience and expertise to Southampton."