A full-tensor, gravity gradient measuring system is disclosed that is based on atom interferometry. Each axis in the three-axis measuring system is served by a different gravity gradiometer, where each gradiometer comprises three pairs of atom interferometric (AI) accelerometers. The accelerometers in each pair are mounted on opposite sides of the gradiometer's rotation axis from each other. The three AI accelerometer pairs are step-rotated, instead of being continuously rotated, thereby providing enhanced signal-to-noise performance. The three gradiometers in the overall measuring system are mounted orthogonally with respect to one another on a local-level platform, in order to achieve a full-tensor measuring system. The measuring system can be step-rotated as an overall unit around an axis perpendicular to a local level reference. The multiple levels of stepped rotation, as enabled by the atom interferometry being utilized, yields improved results with lower costs than what is achievable with some prior-art techniques.