QSM is used to estimate the underlying tissue magnetic susceptibility and oxygen saturation in veins. This paper presents vessel orientation as a new regularization term to improve the accuracy of l1 regularized QSM reconstruction in cerebral veins. For that purpose,the vessel tree is first extracted from an initial QSM reconstruction. In a second step,the vascular geometric prior is incorporated through an orthogonality constraint into the QSM reconstruction. Using a multi-orientation QSM acquisition as gold standard,we show that the QSM reconstruction obtained with the vessel anatomy prior provides up to 40% RMSE reduction relative to the baseline l1 regularizer approach. We also demonstrate in vivo OEF maps along venous veins based on segmentations from QSM. The utility of the proposed method is further supported by inclusion of a separate MRI venography scan to introduce more detailed vessel orientation information into the reconstruction,which provides significant improvement in vessel conspicuity.