Armero, who spent the second half of last season on loan at West Ham United in England, joins Milan on a new loan deal, although the Rossoneri have the option to eventually make the move permanent.
"I spoke to (new Milan coach Filippo) Inzaghi, who as a player loved to win and will want to do the same as a coach," Armero told the Milan Channel before undergoing a medical.
The 27-year-old left-back played in all of Colombia's games during their run to the World Cup quarter-finals last month and scored in their opening 3-0 win against Greece.
His arrival will help Milan in a position where they have seen Dutchman Urby Emanuelson and Guinea's Kevin Constant depart this summer for Roma and Trabzonspor respectively.
He is the second new signing at the San Siro in as many days after goalkeeper Diego Lopez joined from Real Madrid on a four-year deal on Tuesday.
Milan have been busy in the transfer market this summer, with French centre-back Adil Rami, winger Jeremy Menez and Brazilian defender Alex already having been snapped up.
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