The 28-year-old has attracted interest from both the English Premier League and the Italian Serie A after scoring 20 goals in La Liga for Sevilla this past season.
His advisor, Sergio Barila, confirmed earlier this week that the Reds and another English club have declared an interest in Bacca, who was also reportedly being courted by Roma.
But it appears Milan have stolen a march on their rival suitors by agreeing a reported five-year deal for the Colombia international.
Barila told Milan News: "I can confirm that Milan and the player reached an agreement. Carlos chose what is best for his future, so it's only natural he is happy."
Bacca is expected to arrive in Milan next week to undergo a medical, having recently suffered elimination from the Copa America at the quarter-final stages with Colombia after losing to Argentina on penalties.