Puncheon had been on a season long loan deal at Stadium:mk from Plymouth but Southampton signed him for an undisclosed fee on a permanent contract at the weekend.
"I've matured as a player and as a person in the last few years and a lot of that has been down to how welcome Dons fans made me," he told the official Dons website.
"It was a pleasure being part of the Dons squad, they are a fantastic bunch of lads who I am sure will go on and do well.
"But sometimes you have to make decisions in football that you feel are best for your career and Southampton are a massive club with a successful history and I couldn't afford to miss out."