The League One club announced earlier this week that they had made an official approach for the then Hearts boss and after holding talks with the club on Thursday, the Milton Keynes outfit have now announced his arrival after agreeing terms with the Scottish Premiership side.
The 36-year-old told MK Dons PlayerHD: "I'm delighted. It's great to be here and I'm looking forward to developing the club, developing the players and moving the club forward.
"The most important thing for me was picking the right chairman and the right club and this was the right match at the right time – it's a club that's going places.
"Hopefully the fans are ready for the ride. We want to create excitement but, most importantly, win football matches. With the squad that we've got here, we should be winning football matches – our job is to help them do that."
MK Dons currently sit in 19th place in the league table after recording just five wins from 20 games, including no victories in 10 home matches.
Neilson will not officially take charge until after the club's FA Cup tie with Charlton Athletic this weekend.