The 20-year-old midfielder was already in town last night so he could be with the Rossoneri medics from 8.00 local time.
Brescia agreed a deal to loan Tonali for €10m with an option to buy for €15m plus up to another €10m in add-ons.
The Rondinelle will also be guaranteed 10 per cent of any future transfer fee.
He made a strong impression in his debut Serie A season, even though he could not prevent his hometown club from dropping back down to Serie B.
The midfielder already has three senior Italy caps and is pushing for a place at the postponed Euro 2020 tournament.
Inter had agreed a similar deal with Brescia, but delayed the transfer and the player became increasingly frustrated.
A lifelong Rossoneri supporter, he jumped at the chance when Milan came in with a counter-offer.