Smith joins MK Dons from Manchester City
"I’m absolutely delighted to be here and I can’t wait to get going,” he said. "It was time for me to move on away from City and I don’t think I could have found a better club to join. The facilities here are fantastic and the players and staff seem fantastic too. There is a real project going on here and I wanted to be a part of that.
"We’ve got a quality squad who have done really well this season – hopefully I can add to that and help the team achieve its goals."
Head Coach Liam Manning added: "We are very excited to have Matt on board. He is well suited to the way we like to play football, given his upbringing at Manchester City, and is a full Wales international which just highlights the quality he possesses.
"He certainly bolsters our midfield and, I’m sure, he will have a terrific impact between now and the end of the season and beyond that too."