Milan have signed the 23-year-old for a reported inital five million euros ($5.7 million) with an option to buy for a further 35 million euros next summer.
Bakayoko leaves Chelsea after making 29 Premier League appearances for the Blues but failing to recapture the form that prompted the London club to pay Monaco a reported £40 million for his services last summer.
He was left out of the squad by new coach Maurizio Sarri for Chelsea’s opening fixture at Huddersfield on Saturday as his replacement Jorginho scored in a comfortable 3-0 win.
Milan hope Bakayoko will help them reclaim their position at the top of the Italian game following years of strife on and off the pitch.
Last year they finished sixth in Serie A despite the around 200 million euros spent on new players by the disastrous Chinese consortium that bought the club from former Italian Prime Minister Silvio Berlusconi in April 2017.
That led to them falling foul of Uefa’s financial fair play regulations and being booted from this season’s Europa League.
However since hedge fund Elliot Management took control of Milan last month following missed payments from the previous owners, the seven-times European champions have been readmitted to continental competition and have looked to rebuild both the squad and morale.
They have signed proven Serie A goalscorer Gonzalo Higuain from Juventus in a complex deal that also saw them bag promising centre-back Mattia Caldara while offloading the disappointing Leonardo Bonucci back to Juventus.
Meanwhile Milan great Paolo Maldini has been brought in alongside new sporting director Leonardo.