The planned transfer fell through when the necessary paperwork was not delivered in time for Monday's deadline. FIFA declined to approve a request for an exemption.
Dortmund said the two clubs agreed that Grosskreutz would leave for Istanbul immediately, under the previously agreed conditions of the transfer, which were not disclosed.
Grosskreutz will be able to train and play friendlies and will sign when the next transfer period opens on Jan. 1, 2016.