Nantes chief Waldemar Kita says a deal to sell Aston Villa and Liverpool target Jordan Veretout to a Premier League club is "basically agreed".
Charlton have made their seventh signing of the summer by landing defender Naby Sarr from Sporting Lisbon.
It appeared at one stage as if a season-long loan would not happen, with the Holland international initially reluctant to commit to a deal.
Having spent so long sidelined through injury, Van Ginkel was determined to prove his worth to Jose Mourinho and earn a regular role at Stamford Bridge.
He has, however, accepted that a spell in Italy may be of greater benefit in the long run, allowing him to get important minutes under his belt.
Milan are delighted to have him, with another of their summer acquisitions from Chelsea – Fernando Torres – helping to force through a move.
Vice-president Adriano Galliani said at Torres’ unveiling on a two-year loan arrangement: “The most difficult deal was Van Ginkel’s one because he resisted our negotiation, he wanted to be a regular at Chelsea.
“I gave him time to decide and said to (Nigel) De Jong and Fernando Torres to speak with him and convince him to come here. In the end he said yes and he is a great talent.”
Galliani has also revealed that Milan opted against making a fresh approach for Queens Park Rangers playmaker Adel Taarabt – a player who spent the second half of last season on loan in Serie A.
He added: “He wanted to return to Milan and I spoke with him on Monday.
“But we were looking for a different type of player and we chose (Giacomo) Bonaventura.”