Reeves was released by the Saints at the end of the season, but he has revealed that he has selected the right club to continue his career.
The 21-year-old told the club's official website: "It's been an interesting summer, seeing what's around.
"I was at Southampton for 12 years so it's been different looking around other clubs but I'm happy to be here in Milton Keynes.
"I feel that I've definitely picked the right club. I love the way the team play and I'm really looking forward to being part of things here and hopefully help the team push on."
Reeves scored one goal in 13 appearances for Southampton.