  The halo of the Milky Way provides a laboratory to study the properties of
the shocked hot gas that is predicted by models of galaxy formation. There is
observational evidence of energy injection into the halo from past activity in
the nucleus of the Milky Way; however, the origin of this energy (star
formation or supermassive-black-hole activity) is uncertain, and the causal
connection between nuclear structures and large-scale features has not been
established unequivocally. Here we report soft-X-ray-emitting bubbles that
extend approximately 14 kiloparsecs above and below the Galactic centre and
include a structure in the southern sky analogous to the North Polar Spur. The
sharp boundaries of these bubbles trace collisionless and non-radiative shocks,
and corroborate the idea that the bubbles are not a remnant of a local
supernova but part of a vast Galaxy-scale structure closely related to features
seen in gamma-rays. Large energy injections from the Galactic centre are the
most likely cause of both the {\gamma}-ray and X-ray bubbles. The latter have
an estimated energy of around 10$^{56}$ erg, which is sufficient to perturb the
structure, energy content and chemical enrichment of the circumgalactic medium
of the Milky Way.
