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The paper introduces a Data-driven Hierarchical Control (DHC) structure to improve performance of systems operating under the effect of system and/or environment uncertainty. The proposed hierarchical approach consists of two parts: 1) A data-driven model identification component to learn a linear approximation between reference signals given to an existing lower-level controller and uncertain time-varying plant outputs. 2) A higher-level controller component that utilizes the identified approximation and wraps around the existing controller for the system to handle modeling errors and environment uncertainties during system deployment. We derive loose and tight bounds for the identified approximation's sensitivity to noisy data. Further, we show that adding the higher-level controller maintains the original system's stability. A benefit of the proposed approach is that it requires only a small amount of observations on states and inputs, and it thus works online; that feature makes our approach appealing to robotics applications where real-time operation is critical. The efficacy of the DHC structure is demonstrated in simulation and is validated experimentally using aerial robots with approximately-known mass and moment of inertia parameters and that operate under the influence of ground effect.