  High-Frequency Gravitational Waves (HFGWs) constitute a unique window on the
early Universe as well as exotic astrophysical objects. If the current
gravitational wave experiments are more dedicated to the low frequency regime,
the graviton conversion into photons in a strong magnetic field constitutes a
powerful tool to probe HFGWs. In this paper, we show that neutron stars, due to
their extreme magnetic field, are a perfect laboratory to study the conversion
of HFGWs into photons. Using realistic models for the galactic neutron star
population, we calculate for the first time the expected photon flux induced by
the conversion of an isotropic stochastic gravitational wave background in the
magnetosphere of the ensemble of neutron stars present in the Milky Way. We
compare this photon flux to the observed one from several telescopes and derive
upper limits on the stochastic gravitational wave background in the frequency
range $10^8 \, \rm Hz$ - $10^{25}\, \rm Hz$. We find our limits to be
competitive in the frequency range $10^8 \, \rm Hz$ - $10^{15}\, \rm Hz$.
