Snodin made his last appearance in the Athletic dugout last night as Charlton's reserves lost 1-0 to Coventry, ending a six-year reign at The Valley, and he was making his way to St Mary's today after accepting an offer from Burley last week.
Southampton are struggling in the Championship but Snodin has agreed to join the fight to reverse the decline which saw Saints drop from the Premiership last term.
Snodin said: "While Southampton are in a lower league, it's a great step for me in terms of first team coaching and that's the reason behind the move."
Left-back Snodin was brought to Elland Road by Billy Bremner in 1987 from Doncaster and he made 116 appearances before moving north to Scottish club Hearts at the end of United's Division One championship winning season.
Snodin led the Addicks to the FA Premier Reserve League (South) championship in 2004 and 2005.
He added: "Over the last six months or so I've had the feeling in the back of my mind that I wanted to challenge myself again, to see how far I can go."