Milan vice-president Adriano Galliani flew out to Madrid earlier today to complete the deal after weeks of talks.
It's understood that the veteran has signed a two-year deal at the San Siro after Real accepted a fee of around £3.7m.
Former Real and Milan coach Fabio Capello said: "I'm convinced that Milan have got themselves a great buy.
"After a season of highs and lows, Emerson will have a great desire to prove himself again and he will be a very important part of the Rossoneri machine. My compliments go to Milan."