Still, 32, will arrive at St Mary's having guided Lens to an eighth-place finish in France's Ligue 1 this season.
"I’m extremely proud and excited to have joined Southampton – there is huge potential here and we have a great opportunity to do something special," Still told the club's website.
"The project that has been laid out to me is very impressive and, all together, I believe we can build a clear identity and a very positive future for the team.
"I can’t wait to meet you, the fans. I look forward to hearing you in voice, and feeling the energy and belief at St Mary’s and beyond.
"I’m eager to get to work this summer and start building a close-knit group that can make everyone proud and ultimately get us back to where we belong; in the Premier League."