The 24-year-old midfielder has penned a one-year deal at stadium:mk following his release from the now defunct League of Ireland side Sporting Fingal.
Williams, who captained Fingal in last season's Europa League second-round qualifying match against Maritimo, was named as the Professional Footballers' Association of Ireland young player of the year in 2010.
Dons boss Karl Robinson told the club's official website: "I am delighted to have captured the services of Shaun, he was sought after by a number of clubs and it is terrific news that he chose a move to MK Dons would be ideal for his progression.
"At 24 he matches the criteria we are looking for - he is young, ambitious and hungry for success, just like the football club. To be named young player of the year by his fellow professionals shows he is rated in the game and emphasises what we as a management staff already know, we have added another quality player to the club."
The Dons are seeking clarification from FIFA and the Football League as to whether Williams will be able to feature this season.