The Colombian, who was also linked with Roma and Liverpool, will complete the switch pending a successful medical in the Italian capital.
Both Milan and Europa League holders Sevilla confirmed the prospective deal on Thursday.
While neither club disclosed a transfer fee, speculative reports suggest the Rossoneri paid €30 million for Bacca.
The 28-year-old scored 34 goals in 71 appearances for Sevillistas since his arrival from Club Brugge in 2013.