Milan vice-president Adriano Galliani has confirmed that the transfer fee is an initial €18 million (£15m) plus bonuses and add-ons - a clear loss for City on the British record transfer fee splashed out to Real Madrid two years ago.
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The 26-year-old flew into Italy today to pass a medical. He will now join up with fellow new boy Zlatan Ibrahimovic at the San Siro as the club look to recapture the Serie A title for the first time since 2004.
An official statement on the Milan website read: "AC Milan communicates it has acquired the player Robinho, outright from Manchester City. The Brazilian has signed a contract with the Rossoneri club for four years."
Robinho started 48 league and cup matches for the Eastlands outfit and helped himself to 16 goals. After previously rejecting a move to Fenerbahce, he will now look to get his career back on track at the San Siro.
Robinho joins the likes of Ibrahimovic, Ronaldinho, Alexandre Pato in an exciting looking forward line at Milan.