The former Sampdoria striker will ply his trade under Massimiliano Allegri as of the coming season, while his former Blucerchiati teammate has moved in the opposite direction.
Reports in Italy have also suggested that the Rossoneri have paid their city rival an additional 7 million euros for the transfer to go through.
Both clubs already reached an agreement over a swap on Monday evening, with both players undergoing medicals at their respective new clubs the following day, and the deal has now been made official.
Milan was in the market for a new target man following the departure of Zlatan Ibrahimovic to Paris Saint-Germain, and head coach Massimiliano Allegri has now got his man in Pazzini.
The 28-year-old was no longer needed at Inter as Andrea Stramaccioni did not see the forward in his first-team plans, and he will now continue his career with the red side of San Siro.
Cassano, meanwhile, filed a transfer request as he felt Milan showed a lack of ambition by letting go of several key players this summer, and has jumped at the opportunity of joining the club he supported as a child.
The Italy forward, 30, has signed on with Inter until the summer of 2014 and was welcomed by Stramaccioni and captain Javier Zanetti on the training pitch on Wednesday morning.
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