Neutrino telescope IceCube has recently discovered astrophysical neutrinos with energies in the TeV – PeV range .
We use the data of Fermi \gamma -ray telescope to demonstrate that the neutrino signal has significant contribution from the Milky Way galaxy .
Matching the \gamma -ray and neutrino spectra we find that TeV-PeV Galactic cosmic rays form a powerlaw spectrum with the slope p \simeq 2.45 .
This spectral slope is consistent with the average cosmic ray spectrum in the disks of the Milky Way and Large Magellanic Cloud galaxies .
It is also consistent with the theoretical model of cosmic ray injection by diffusive shock acceleration followed by escape through the Galactic magnetic field with Kolmogorov turbulence .
The locally observed TeV-PeV cosmic ray proton spectrum is softer than the average Galactic cosmic ray spectrum .
This could be readily explained by variability of injection of cosmic rays in the local interstellar medium over the past 10 ^ { 7 } yr and discreetness of the cosmic ray source distribution .