The Sunderland striker will make the move after an agreement was reached between Milan and Sunderland, with official confirmation to come soon, Sky Sports reported.
The Rossoneri, and Serie A rivals Roma, were said to be interested in signing the 26-year-old during the January transfer window, but Sunderland rebuffed their advances as they wanted to keep the player as they fought for Premier League survival.
Borini started 19 Premier League games for the Black Cats last season, netting two goals and notching two assists.
The one-cap Italy international joined Sunderland from Liverpool for £14m in the summer of 2014 after registering two goals in 25 appearances at Anfield.
Borini’s departure would be the second high-profile transfer from relegated Sunderland after goalkeeper Jordan Pickford joined Everton last month for £30m.
England international Jermain Defoe is also reported to be on the move, with Bournemouth and former club West Ham interested.