Torres replaces Mario Balotelli as Milan's main striker following the Italian's £16 million switch to Liverpool, with the transfer subject to personal terms and a medical which will take place on Saturday.
The Spanish international has struggled badly since joining Chelsea from Liverpool in January 2011 for a then-British record £50 million fee, scoring just 45 goals in 172 appearances.
He had previously netted 81 times in 142 games during his three-and-a-half seasons with Liverpool, with his Blues record equating to a sizeable £1.1 million per goal.
His future the subject of on-going speculation over the summer, Torres had two years left on his £150,000-a-week deal at Stamford Bridge, and it had been feared that Milan’s struggles to match his demands would see the deal collapse.
However, the 30-year-old’s representatives are said to have negotiated a hefty severance package in order to make the move possible, with Chelsea's attacking options now down to Diego Costa and Didier Drogba.
Jose Mourinho had earlier claimed that he wanted to keep Torres to ensure that he had enough options up top, but the deal could allow the Portuguese manager to bring in additional firepower from elsewhere.
The club have been linked with both Queens Park Rangers’ Loic Remy and Roma’s Mattia Destro in recent days, with the transfer window set to close on Monday night.