Walker is leaving City this month, with manager Pep Guardiola confirming last week the fullback had made a transfer request.
Il Corriere dello Sport says there is already an agreement with Milan: the 33-year-old will earn €5m net per season until 2027.
Despite his 33 years, the Rossonero consider him a valuable reinforcement for his experience, personality and tactical versatility.
Walker, capable of playing in a three-man defense, will terminate his contract with City before it expires in June.
The farewell party organised by the player and Guardiola's words confirm his imminent departure.