Torres had made the same move just 24 hours earlier after agreeing a two-year loan stay at San Siro, ending weeks of tough negotiations between the two sides.
And van Ginkel was announced as Milan's newest recruit late last night despite the player having reportedly rejected Milan last week.
After that call, van Ginkel reconsidered his position and within hours had given his consent to join AC Milan.
La Gazzetta dello Sport reports that Milan will pay Chelsea around £315,000 for the loan but if van Ginkel plays more than 20 games then that sum will be almost doubled.
The deal represents another coup for Milan vice-president Adriano Galliani, who has been severely tested in this market by the Rossoneri's failure to secure European football for this season.