The vertebral column is a complex anatomical construct, composed of vertebrae and intervertebral discs (IVDs) supported by ligaments and muscles. During life, all components undergo degenerative changes, which may in some cases cause severe, chronic and debilitating low back pain. The main diagnostic challenge is to locate the pain generator, and degenerated IVDs have been identified to act as such. Accurate and robust segmentation of IVDs is therefore a prerequisite for computer-aided diagnosis and quantification of IVD degeneration, and can be also used for computer-assisted planning and simulation in spinal surgery. In this paper, we present a novel fully automated framework for supervised segmentation of IVDs from three-dimensional (3D) magnetic resonance (MR) spine images. By considering global intensity appearance and local shape information, a landmark-based approach is first used for the detection of IVDs in the observed image, which then initializes the segmentation of IVDs by coupling deformable models with convolutional networks (ConvNets). For this purpose, a 3D ConvNet architecture was designed that learns rich high-level appearance representations from a training repository of IVDs, and then generates spatial IVD probability maps that guide deformable models towards IVD boundaries. By applying the proposed framework to 15 3D MR spine images containing 105 IVDs, quantitative comparison of the obtained against reference IVD segmentations yielded an overall mean Dice coefficient of 92.8%, mean symmetric surface distance of 0.4 mm and Hausdorff surface distance of 3.7 mm.