The MLS club have announced the departure of the defender, who has impressed in recent months.
Binks was a part of the Spurs academy and played for their under-23 side.
He moved to Canada in February for regular game time, and was impressive in the MLS games he played.
Now the 18-year-old is permanently transferring to Bologna.
However, he will stay at Montreal on loan until 2021, as the two clubs share an owner.
"We had an opportunity to see his quality last winter during his first four games with the Impact and more recently in Florida, and we're excited for him to join us.
"This transfer once again demonstrates the synergy between the two clubs and the new philosophy in place in Montreal."