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. 

Speaking to Sky Italia, Kaka expressed his delight at returning to the Serie A club.

"I'm coming home," he said.

"'I'm very happy. And now I get to live lots of new joyous moments with Milan."

Kaka could make his second Milan debut for the club against Torino on September 15.