An endovascular graft, e.g., having both an expandable stent portion and a stent cover portion positioned within and/or surrounding the expandable portion, the graft itself and/or a stent cover portion being coated with a bioactive agent adapted to promote initial thrombus formation, preferably followed by long term fibrous tissue ingrowth. The endovascular graft addresses concerns regarding endoleaking by permitting the graft to be deployed and used in a manner that promotes a short term hemostatic effect in the perigraft region. This short term effect can, in turn, be used to promote or permit long term fibrous tissue ingrowth. Particularly where the stent cover portion is prepared from a porous material selected from PET and ePTFE, the bioactive agent can include a thrombogenic agent such as collagen covalently attached in the form of a thin, conformal coating on at least the outer surface of the stent cover. An optimal coating of this type is formed by the activation of photoreactive groups provided by either the cover material itself, by the bioactive agent itself, and/or by a linking agent.