Walker will leave City this month, with manager Pep Guardiola confirming last week that the full-back had made a transfer request.
Il Corriere dello Sport says there is already an agreement in place with Milan: the 33-year-old will earn a net €5 million per season until 2027.
Despite his 33 years, the Rossonero consider him a valuable addition due to his experience, personality and tactical versatility.
Walker, who can play in a three-man defence, will end his contract with City before it expires in June.
The farewell party organized by the player and Guardiola's words confirm his impending departure.
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