The treatment of degenerative spinal disorders requires an understanding of the individual spinal anatomy and curvature in 3D. An upright spinal pose (i.e. standing) under natural weight bearing is crucial for such bio-mechanical analysis. 3D volumetric imaging modalities (e.g. CT and MRI) are performed in patients lying down. On the other hand, radiographs are captured in an upright pose, but result in 2D projections. This work aims to integrate the two realms, i.e. it combines the upright spinal curvature from radiographs with the 3D vertebral shape from CT imaging for synthesizing an upright 3D model of spine, loaded naturally. Specifically, we propose a novel neural network architecture working vertebra-wise, termed \emph{TransVert}, which takes orthogonal 2D radiographs and infers the spine's 3D posture. We validate our architecture on digitally reconstructed radiographs, achieving a 3D reconstruction Dice of $95.52\%$, indicating an almost perfect 2D-to-3D domain translation. Deploying our model on clinical radiographs, we successfully synthesise full-3D, upright, patient-specific spine models for the first time.