To date, 3D spine reconstruction from biplanar radiographs involves intensive user supervision and semi-automated methods that are time-consuming and not effective in clinical routine. This paper proposes a new, fast, and automated 3D spine reconstruction method through which a realistic statistical shape model of the spine is fitted to images using convolutional neural networks (CNN). The CNNs automatically detect the anatomical landmarks controlling the spine model deformation through a hierarchical and gradual iterative process. The performance assessment used a set of 68 biplanar radiographs, composed of both asymptomatic subjects and adolescent idiopathic scoliosis patients, in order to compare automated reconstructions with ground truths build using multiple experts-supervised reconstructions. The mean (SD) errors of landmark locations (3D Euclidean distances) were 1.6 (1.3) mm, 1.8 (1.3) mm, and 2.3 (1.4) mm for the vertebral body center, endplate centers, and pedicle centers, respectively. The clinical parameters extracted from the automated 3D reconstruction (reconstruction time is less than one minute) presented an absolute mean error between 2.8° and 4.7° for the main spinal parameters and between 1° and 2.1° for pelvic parameters. Automated and expert's agreement analysis reported that, on average, 89% of automated measurements were inside the expert's confidence intervals. The proposed automated 3D spine reconstruction method provides an important step that should help the dissemination and adoption of 3D measurements in clinical routine.