Intervertebral prosthetic devices and methods of implanting the same within an intervertebral space between adjacent vertebral bodies are provided. One device includes first and second components, each configured to engage a respective one of the adjacent vertebral bodies. Each component includes a vertebral support plate with a spherical segment protruding therefrom. The spherical segments are disposed to reside within nuclear recesses in the adjacent vertebral bodies when the device is implanted in the intervertebral space, and are configured with a common center of rotation which aligns with the natural axis of rotation of the adjacent vertebral bodies. An articulation member, which interfaces the first and second vertebral support plates, may be an articular ball and respective concave articular surface regions in the plates, or alternatively, a convex articular surface and a respective concave articular surface in the vertebral support plates of the first and second components.