The 21 year-old spent last term with Colchester on-loan.
Lawrence said: "I sat down with (Southampton Manager) Russell Martin for 20-30 minutes to discuss my options, and what would suit me best and help me thrive the most, and obviously it was MK!
"The style of play is something that excites me a lot, it's similar to Southampton's style of football, I can't wait to kick-start and get going!"
Dons boss Mike Williamson also told the club's website: "Nico is a highly-rated young player who had a few options this summer, so I'm delighted he's chosen to come here and Southampton have trusted us with his continued development.
"He possesses the ball skills and vision required to be a real asset to our defence but also has the physicality to compete in League Two, we're very pleased to have him."