According to Mail Online Football, the 51-year-old Austrian penned a two-and-a-half year contract with the club and will take over from caretaker manager Kelvin Davis on Thursday, after the game against Spurs.
He replaces Mark Hughes who was sacked on Monday after an awful start to the season, winning just one win match out of 14 games this season.
His assistant first team manager Mark Bowen and assistant first team coach Eddie Niedzwieck also left the club with him.
In a statement by Southampton chairman Ralph Krueger, he said: ‘The urgency to find a path back to our potential and to the results that we expect cannot be underestimated.
‘For that reason, we are extremely pleased that Ralph Hasenhuttl has agreed to become our new manager and do all he can to help guide us back on that path.
‘This manager change offers us a fresh start and, very quickly, Ralph emerged as our ideal candidate.
‘As a coach, he embodies the passion, structure, communication skill set, work ethic and appetite for growth that we strive for in our Southampton Way.
‘The quick, smooth and seamless negotiation process underlines the character of the person that he is.
‘We have been aware of Ralph since his days at Ingolstadt, where he showed the qualities that we believe we need at the club.
‘He has since gone on to develop those attributes with a track-record of success in the Bundesliga and with a progressive and ambitious club in RB Leipzig
‘As soon as we met, Ralph’s enthusiasm for football was contagious and his hunger to take on a new and challenging job in the Premier League was evident.