The visitors had secured their place with a 1-0 weekend defeat of Luxembourg, but this result left Marco van Basten's side in second place behind Romania.
Huntelaar becomes the latest in a long list of Dutchmen to join the Rossoneri, following in the footsteps of Marco van Basten, Ruud Gullit and Frank Rijkaard.
Van Basten has agreed to rest Manchester united goalkeeper Edwin van der Sar but there is still no place in the Holland squad for Real Madrid striker Ruud van Nistelrooy.
Marco van Basten's team had gone into the quarterfinal match off the back of three convincing victories, but failed to reproduce their captivating football of the group stages and could have no complaints about the outcome.