The 27-year-old midfielder’s Inter career has stalled since a bright start in his first season after joining from Portsmouth in 2008.
While initially a first choice starter under Jose Mourinho, he fell out of favour in the next campaign and has never managed to regain a regular starting berth.
He spent the second half of last season on loan at Sunderland, although that too didn’t work out.
He made only four appearances for Inter this season and has now decided to move on, although as he is on Africa Cup of Nations duty he won’t be able to play for the club until Ghana are eliminated.
Milan boss Massimiliano Allegri believes this is the move Muntari needs to kick-start his career.
“This is an important chance for him having not done well at Inter,” said Allegri.
“He’s a good player, so far he’s not fulfilled his technical and physical qualities.”
Muntari began his professional career at Udinese before moving to Portsmouth after five successful years in Italy.
But after just one season at Portsmouth Mourinho came calling when he took over at Inter.
But that move soon turned sour, despite Muntari being part of the treble winning squad in 2010.