The 21-year-old made just one first-team appearance for the Canaries after joining them from Falkirk in 2014.
He moved to Norwich after scoring eight goals in 82 games for Falkirk, and will move to Stadium:MK on two-year deal when his Norwich contract ends in June.
McGrandles played alongside Dons manager Robbie Neilson during his time with Falkirk.
"When I learnt MK Dons were interested, I knew that it would be a great place for me to come to," McGrandles told the club website.
"I know the ambition of the club is to get out of the league again and that was a big factor. I know the manager and the coaching staff well too so that was another big draw."
McGrandles was among a group of Norwich youngsters released earlier in the month, with the announcement coming shortly after their first-team retained list was published.
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League One side MK Dons have signed midfielder Conor McGrandles on a free transfer from Norwich City.