Atalanta finished third in last season's Serie A, above Inter and Milan who were fourth and fifth respectively, which qualified them directly for next season's Champions League group stage.
It will be the first time in Atalanta's history participating in Europe's showpiece event.
Unfortunately, their own home ground, the Stadio Atleti Azzurri d'Italia in Bergamo, doesn't meet UEFA standards and is currently undergoing renovations which won't be finished in time.
In the UEFA Europa League last season they used the Mapei stadium of fellow Serie A club Sassuolo for all their home matches, but San Siro (officially the Stadio Giuseppe Meazza) is bigger, more prestigious, and even closer to home - just a 45-minute drive away.
With Milan disqualified from European competition for Financial Fair Play breaches, the opportunity to use San Siro midweek next season arose.
Despite public urging by fans of both Milanese clubs to refuse Atalanta's request, it was confirmed on Friday (AEST) that permission had been granted.
There has been significant backlash from club ultras, Inter's Curva Nord and the Curva Sud of Milan.
“A wicked choice. Atalanta in Milan, no thanks," wrote the Inter fans.
"Absurd choice, dictated by personal interests and one that tramples over all logic.”
The Milan supporters had a similar message: "In the football we love, this request would have been returned to sender with a good, long laugh.
"Percassi’s (Atalanta president) request offends us Rossoneri fans. San Siro is our home.”
AC Milan, the last party to consent, stated "We believe this opportunity is beneficial not only for Atalanta but also all of Italian football as it is inspired by important values such as the sense of hospitality, respect and ‘fair play’.”
Atalanta captain Alejandro 'Papu' Gomez took to social media to offer his thanks, saying: "On behalf of my teammates, we want to thank Inter and Milan for welcoming us to their glorious stadium."
"For us it’s essential not to make long trips, especially in such a demanding competition.
"It will be an honour to play at San Siro, we will give the best of ourselves. Thank you so much.”