The Heed boss leaves the International Stadium to take the League Two job after MK acted speedily having parted company with Graham Alexander on Monday.
The former Newcastle United defender has a growing reputation in the game and has earned an increasing number of admirers with an eye-catching style of play.
A formal approach was "reluctantly accepted" after Williamson "had expressed his desire to pursue negotiations" the club have said tonight.
Rob Elliott, Louis Storey and Carl Magnay have also taken charge on a temporary basis.
Gateshead romped to the National League North title in 2022 and then were beaten FA Trophy finalists last season in a campaign where the club were comfortably mid-table.
With the North East side sitting in a play-off position and in the first round of the FA Cup, they will now move to replace Williamson and to keep their so-far impressive season on track.
Chairman Neil Pinkerton said: “Mike has been a fantastic servant to Gateshead Football Club and agreed to re-join the club, alongside Ian and Chris, at a time when we didn’t have a single contracted player following our demotion in 2019.
“The success they have brought to our club is testament to them as individuals and as a collective team, of which there are many more.
“An approach from MK Dons – a club in the EFL that was only recently in the Championship – proved too much to turn down and we wish them every success, of which we are sure they will be.”