The Spain international has endured a troubled career at Stamford Bridge, struggling for form and goals following his £50 million move from Liverpool, but will now stay with the Rossoneri until 2016.
Goal reported the San Siro outfit's interest earlier this week and, despite fears that the deal could collapse over the striker's £170,000-a-week wages, the two sides have worked hard to reach an agreement.
The move, however, is subject to personal terms and a medical, with Torres now en route to Milan to undergo tests on Saturday and finalise details for a move to the San Siro.
Torres scored just 20 Premier League goals in 110 matches for Chelsea, though played a role in the club's stunning Champions League win in 2011-12 as they defeated Bayern Munich on 4-3 penalties.
Chelsea are now likely to be on the hunt for a new striker before the transfer window slams shut, with Jose Mourinho having previously insisted that he would need three forwards this season.
The west Londoners had been linked with Roma's Mattia Destro, but the Italian side's president, James Pallotta, has denied that the striker will be allowed to leave.
Torres' departure ensures Mourinho has an entirely new frontline compared to last season, with Diego Costa and Didier Drogba replacing the Spaniard, Demba Ba, Samuel Eto'o and Romelu Lukaku this summer.