The 37-year-old, who was player-coach at the League One club, has become part of Sven-Goran Eriksson`s backroom team, replacing Chris Powell who left to take over as manager of Charlton last month.
A statement on the Dons' official website said: "The club can confirm that Dietmar Hamann has left his post as first-team coach to take up a position with Leicester.
"Everyone at MK Dons would like to place on record our thanks to Didi for his hard work. We wish him well in his emerging coaching career."
Hamann played under Eriksson when the Swede was in charge at Manchester City. He left Eastlands in 2009 and joined MK Dons a year later.
Hamann moved to England in 1998, playing one season at Newcastle before joining Liverpool.
He scored the final goal at the old Wembley as Germany beat England 1-0 - a result which led to then-England boss Kevin Keegan resigning, with Eriksson taking over.