The Large Magellanic Cloud is the most massive satellite galaxy of the Milky Way, with an estimated mass exceeding a tenth of the mass of the Milky Way1,2,3,4,5. Just past its closest approach of about 50 kpc, and flying past the Milky Way at an astonishing speed of 327 km s−1 (ref. 6), the Large Magellanic Cloud can affect our Galaxy in a number of ways, including dislodging the Milky Way disk from the Galactic centre of mass7,8,9. Here, we report evidence that the Milky Way disk is moving with respect to stellar tracers in the outer halo in a direction that points at an earlier location on the Large Magellanic Cloud trajectory. The resulting reflex motion is detected in the kinematics of outer halo stars and Milky Way satellite galaxies with accurate distances, proper motions and line-of-sight velocities. Our results indicate that dynamical models of our Galaxy cannot neglect gravitational perturbations induced by the Large Magellanic Cloud infall, nor can observations of the stellar halo be treated in a reference frame that does not correct for disk reflex motion. Future spectroscopic surveys of the stellar halo combined with Gaia astrometry will allow for sophisticated modelling of the Large Magellanic Cloud trajectory across the Milky Way, constraining the dark matter distribution in both galaxies with unprecedented detail.