The former Lazio sports director is set to take up a similar role with the Rossoneri.
La Gazzetta dello Sport says Tare has signed a three-year contract with Milan and his appointment will soon be made public.
Tare takes charge as Milan miss qualifying for European football this season, with a complete squad rebuild needed.
The Albanian is also expected to be in charge of finding a replacement for coach Sergio Conceicao, who is set to leave after today's season finale against Monza.