  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 Way.
Just past its closest approach of about 50 kpc, and flying by the Milky Way at
an astonishing speed of 327 km/s, the Large Magellanic Cloud can affect our
Galaxy in a number of ways, including dislodging the Milky Way disc from the
Galactic centre-of-mass. Here, we report evidence that the Milky Way disc is
moving with respect to stellar tracers in the outer halo ($40<r<120$ kpc) at
$v_{\rm travel}=32^{+4}_{-4}$ km/s, in the direction $(\ell,b)_{\rm
apex}=(56^{+9}_{-9},-34^{+10}_{-9})$ degrees, which points at an earlier
location on the LMC 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 disc
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.
