The Daily Mail says Adkins, 45, who earned less than £100,000 at Glanford Park, signed a three-year contract deal worth £200,000 pounds-a-year to replace sacked Alan Pardew.
The former physio has also been promised a huge bonus for getting Saints back into the Premier League by the end of his contract.
Adkins, who was forced to put his move to St Mary's on hold last week awhile the two clubs haggled over compensation, said: "I am delighted to be the manager of Southampton. It's a very proud honour to join a club with such a big tradition.
"I'm really looking forward to this fresh challenge and I'm very optimistic of where we can take this club.
"We want to excite the supporters, because when this stadium is full I am sure there is a fantastic buzz, so I hope the supporters are looking forward to watching their team winning in the right style."