The Saints battled back from two goals down to draw 2-2 at Chelsea in midweek and are currently in 15th place in the Premier League table.
Adkins, who spent two-and-a-half years in charge at Southampton, guided the Saints into the Premier League last season.
“The club would like to thank Nigel Adkins for his service over the past three seasons, and wish him well for the future,” said a Southampton spokesman.
Pochettino, 40, who will take charge against Everton on Monday said: “This is the kind of opportunity that any coach would relish.
“Southampton is a club with great heritage, and an even more exciting future.
“There is a clear vision to take the club to a new era of sustained success in the Premier League, and beyond, which I’m delighted to be part of.”
Southampton chairman Nicola Cortese said the decision to replace Adkins with Pochettino has been made in the “long-term” interests of the club.
The Italian 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.”
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