The 27-year-old Colombia international, who spent six months on loan with Premier League club West Ham this year, will join the Rossoneri on a season-long loan should he pass the required tests.
Armero told Milan's official website: "I am joining a great team.
"I've spoken to coach (Filippo) Inzaghi, he was a footballer who loved to win and he wants to do the same as a coach.
"He's told me I have to work with intensity and give my all in order to become a first-team regular."
Armero joined Napoli from Udinese on a permanent basis last summer but was restricted to making only 14 Serie A appearances for the Stadio San Paolo outfit during the 2013-14 season.