Astronomical telescopes suffer from a tradeoff between field-of-view (FoV) and image resolution: increasing the FoV leads to an optical field that is under-sampled by the science camera. This work presents a novel computational imaging approach to overcome this tradeoff by leveraging the existing adaptive optics (AO) systems in modern ground-based telescopes. Our key idea is to use the AO system’s deformable mirror to apply a series of learned, precisely controlled distortions to the optical wavefront, producing a sequence of images that exhibit distinct, high-frequency, sub-pixel shifts. These images can then be jointly upsampled to yield the final super-resolved image. Crucially, we show this can be done while simultaneously maintaining the core AO operation --- correcting for the unknown and rapidly changing wavefront distortions caused by Earth's atmosphere. To achieve this, we incorporate end-to-end optimization of both the induced mirror distortions and the upsampling algorithm, such that telescope-specific optics and temporal statistics of atmospheric wavefront distortions are accounted for. Our experimental results with a hardware prototype, as well as simulations, demonstrate significant SNR improvements of up to 12 dB over non-AO super-resolution baselines, using only existing telescope optics and no hardware modifications. Moreover, by using a precise bench-top replica of a complete telescope and AO system, we show that our methodology can be readily transferred to an operational telescope.