De Jong had just one year remaining on his City contract and had found himself pushed down the pecking order following the arrival of Jack Rodwell.
"I am very happy that I will play for AC Milan," he said. "Milan will compete, both in Italy and in Europe.
"I am very happy with this transfer to a fascinating club with a great history.
"Following the Manchester derby I can now look forward to the Milan derby."
It is thought that the Dutch international will undergo a medical and complete formalities before an official presentation tomorrow.