The 31-year-old spent six years at San Siro between 2003 and 2009 before moving to Real Madrid for a then world-record fee of around €65million.
During his time at the Santiago Bernabeu, Kaka won three trophies - one La Liga title, the Copa del Rey as well as a Supercopa de Espana.
However, the Brazil international found himself out of favour under new Real manager Carlo Ancelotti this season, and expressed a desire to leave the club last week after failing to feature in La Liga this campaign.
He could make his second Milan debut for the club against Torino on September 15.
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