The 33-year-old former Manchester United and Real Madrid player is believed to have part-funded his move to Milan himself.
It has certainly worked out well for both club and player, as he has made 13 league appearances so far for Milan and has moved back into contention as a major player for England, who are coached by former Milan coach Fabio Capello.
"Our agreement with the Galaxy is very clear," said Galliani.
"We obtained what we desired, which was to keep David until the end of the season."
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