An x-ray velocimetry technique is described which provides three components of velocity measurement in three dimensional space. Current x-ray velocimetry techniques, which use particle images taken at a single projection angle, are limited to two components of velocity measurement, and are unable to measure in three dimensions without a priori knowledge of the flow field. The proposed method uses multiple projection angles to overcome these limitations. The technique uses a least-squares iterative scheme to tomographically reconstruct the three-dimensional velocity field directly from two-dimensional image pair cross-correlations, without the need to reconstruct three-dimensional particle images. Synchrotron experiments demonstrate the effectiveness of the technique for blood flow measurement in opaque vessels, with applications for the diagnosis and treatment of cardiovascular disease.