The Spaniard's move is subject to him agreeing personal terms and passing a medical on Saturday.
The ex-Liverpool and Atletico Madrid forward joined Chelsea for a then-British record £50m in January 2011.
Torres scored 20 goals in 110 league appearances during his spell at Stamford Bridge.
He scored 65 goals in 102 league appearances during his time in Merseyside.
Manager Jose Mourinho said: "If he wants to leave, it's because he wants to try a new life, a new club, probably a new league."
Torres had struggled during his time at Chelsea, finding first team appearances limited.
His prospects were hampered further by the arrival of fellow countryman Diego Costa from Atletico Madrid this summer.
Costa and Didier Drogba remain Chelsea's attacking options.
Biggest transfer fees paid by a British club
Angel Di Maria
Real Madrid to Manchester Utd
Liverpool to Chelsea
Real Madrid to Arsenal
Atletico Madrid to Manchester City
Chelsea to Manchester Utd
Newcastle to Liverpool
Barcelona to Arsenal
The Italian giants are looking for another forward to replace Mario Ballotelli, who left the club for Liverpool on 23 August.
Speaking on Milan's official website on Wednesday, Rossoneri vice-president Adriano Galliani said: "Torres is certainly an important forward and we will see if we can sign him or another player."
Torres's British record transfer fee stood until Angel Di Maria moved from Real Madrid to Manchester United for £59.7m this week.
Fernando Torres's goalscoring record at Chelsea
72 (38) appearances 20 goals
7 (6) appearances 4 goals
5 (1) appearances 3 goals
Other (including European competitions)
33 (10) appearances 19 goals