The Spanish youngster reached the targets set to make his loan into an outright signing this week.
Apart from Milan, also enjoying a windfall is Real Madrid, which allowed Jimenez to leave for the Rossoneri in 2014.
Under a clause agreed upon when he left Real Madrid, the club will receive 50 per cent of the transfer fee, amounting to approximately €13m.
Bournemouth will pay a fixed fee of €20m plus up to €6m in add-ons for the permanent signing of Jiménez, who has signed a long-term contract until June 2031.
Bournemouth chief Tiago Pinto said: "He has had an impressive career, beginning his development at both Real Madrid and AC Milan.
"We are very happy to have him in our project, which began last summer and continues now that the transfer has been finalise."