A method for endothelial keratoplasty donor tissue transport and delivery to a recipient's eye, such as in DLEK, DSEK and DSAEK procedures, comprises the steps of: attaching endothelial keratoplasty donor tissue to a tissue holder, wherein the attachment between the tissue holder and the donor tissue is not on the endothelial layer of the endothelial keratoplasty donor tissue; placing the tissue holder and the attached donor tissue within a surrounding insertion tip; transporting the insertion tip to a position adjacent an access opening in the recipient's eye; inserting the tissue holder with the attached donor tissue through the opening and extending the tissue holder from within the insertion tip to position the donor tissue within the recipient's eye; and separating the attached donor tissue from the tissue holder with the tissue holder within the recipient's eye. An associated apparatus is disclosed.