The 51-year-old Austrian, who succeeds Mark Hughes, has agreed a two-and-a-half-year deal and will take charge on Thursday.
The Saints parted company with Hughes on Monday having won only one of their 14 Premier League games this season and lying 18th in the table.
Former RB Leipzig coach Hasenhuttl was available after ending his impressive spell with the German club in the summer. He previously coached at Unterhaching, Aalen and Ingolstadt.
Southampton chairman Ralph Krueger 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 FC 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.
“In our discussions, he very quickly aligned himself with the values and the vision of the club.
“Southampton Football Club’s past success was built on a clear identity. The foundation of this identity was a focus on developing players, whether from within our academy or after joining from other clubs.
“Ralph’s ability to teach the game and to develop talent is evident in his past and is a centrepiece of why he is the perfect choice to be the new Saints manager.”
Hasenhuttl became Leipzig boss in the summer of 2016, with them having just secured promotion to the Bundesliga, and he guided them to a second-placed finish the following season.
Last term they came sixth, as well as reaching the Europa League quarter-finals.
Hasenhuttl will be supported at Southampton by existing first-team assistant coach Kelvin Davis, head of goalkeeping Dave Watson and head of sports science Alek Gross.
Davis will be in charge of the team for Wednesday evening’s clash with Tottenham at Wembley.
Know more about Sport360 Application