Adkins and his assistant Andy Crosby accepted an offer to take charge at St Mary's last week, but were unable to move before the weekend as the two clubs negotiated on a fee to release them from their Iron contracts.
Talks broke down on Thursday, with Adkins and Scunthorpe United believing the offer from the Saints had been withdrawn. Despite offering the job to Bournemouth's Eddie Howe, that was not the case and - despite a delay as Nicola Cortese, the Southampton chairman, went to Switzerland - a deal was settled on over the weekend.
"It's a very proud honour for myself, and Andy Crosby who is joining me as assistant manager, to join a club with such a big tradition," said Adkins
"I'm proud to have been given the opportunity by the chairman, Nicola Cortese, and look forward to taking the football club forward. I'm looking forward to this fresh new challenge, and I'm very optimistic of where we can take this football club."
Ian Baraclough is expected to take charge of the Iron's first-team in a caretaker capacity, with his first focus to prepare the side ahead of a trip to Sheffield United on Tuesday evening.
Adkins spent 14 years at Glanford Park, initially joining as physiotherapist. He was elevated to manager in November 2006 following the departure of Brian Laws to Sheffield Wednesday.
His time in charge were among the best in the Iron's history - winning promotion from League One twice.
"Nigel stood out from the start. He was at the forefront of my mind throughout the interview process, and the only manager that we offered the job to, so I am extremely happy that both Nigel and Andy have agreed to join us," said Cortese.
"What is clear from the excellence of the applicants is that the outside world is now beginning to acknowledge the quality of new thinking and ideas we are applying at Southampton.
"Nigel has a strong record of developing players and strong beliefs on how the game should be played, in a fast attacking style. He is clearly an extremely loyal, ambitious and committed man who is a very good communicator and mentor to players. I look forward to working with him. "
Cortese's comments countered claims from Bournemouth that Eddie Howe, their manager, was offered the Saints job on Thursday morning when talks over compensation between them and the Iron appeared to break down.