Jones comes in as a replacement for Ralph Hasenhuttl, who was sacked on Monday after almost four years in charge, with the Saints stuck in the bottom three of the Premier League table.
Southampton had to agree a compensation package with Luton Town to price Jones away from the Championship club.
Jones was named Championship manager of the year last season after guiding Luton Town into the play-offs.
"I'm really proud to be given this opportunity. I know a lot about the club from back in the days of The Dell, to coming here to St Mary's, and it's a wonderful football club," Jones told Southampton's official website.
"A lot of my family are Southampton fans, which doesn't half help, and I feel really, really proud to be given the opportunity, and I'm really looking forward to getting started.
"Obviously, I wanted to manage in the Premier League, I've dreamt of that since I've become a coach or a manager, but this club in particular - because of how it's run, because of the structure, because of how they look deeper than just results - really appeals to me."
Jones takes his new side to Anfield to face Liverpool in the Premier League on Saturday.
