The dismissal comes two days after Saints fought back from two goals down to draw 2-2 with European champions Chelsea as part of a turnaround in fortunes in a run where they have lost just twice in their last 12 Premier League games.
Manchester United manager Sir Alex Ferguson was among those to raise eyebrows at the decision, saying it was a "crazy world", while others questioned whether Pochettino was the right man for the job having never played or coached in England.
"This decision has been made with the long-term ambitions of Southampton Football Club in mind," executive chairman Nicola Cortese said in a statement on the club's website.
"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."
"I just find it had to believe," United manager Ferguson told a news conference.
"You get a really good result on Wednesday, 2-0 down and come back to 2-2, look there's no point saying I'm surprised because it's a crazy world and some strange things happen in the game of football but it does seem very unfair."
Former Southampton captain Matt Le Tissier said Adkin's departure had come at a strange time in the season.
"I think everybody will be taken aback by it all I suppose, the club seemed to have come to terms with life in the Premier League, it was a tough start but they then turned things around pretty well," he told Sky Sports News.
"Mauricio is a well-respected coach of substantial quality who has gained a reputation as an astute tactician and excellent man manager," Cortese said.
"I have every confidence that he will inspire our talented squad of players to perform at the highest possible level."
Pochettino's first game in charge will be Monday's Premier League at home to Everton.
"This is the kind of opportunity that any coach would relish," the former Argentina international said in a statement.
"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."
"With due respect to Pochettino, what does he know about our game? What does know about the Premier League? What does he know about the dressing room? Does he speak English?" the BBC quoted him as saying.
Pochettino, a former centre-back, spent most of his playing days at Espanyol with spells also at Argentine club Newell's Old Boys and French sides Paris Saint-Germain and Bordeaux.
