The Spaniard is out of contract at Napoli at the end of the season and he has rejected their new deal.
The Serie A leaders were offering the 35-year-old a 12-month extension and he was unhappy with the length of those terms.
And Reina has now instead, according to Tuttosport, agreed to join Milan in July.
The former Liverpool goalkeeper will sign a two-year deal worth around £40,000-a-week.
The contract also contains the option to extend Reina’s stay for a third year if both he and Milan choose to do so.