We present a solution for the ultraviolet - submillimetre (submm) interstellar radiation fields (ISRFs) of the Milky Way (MW), derived from modelling COBE, IRAS and Planck maps of the all-sky emission in the near-, mid-, far-infrared and submm. The analysis uses the axisymmetric radiative transfer model that we have previously implemented to model the panchromatic spectral energy distributions (SEDs) of star-forming galaxies in the nearby universe, but with a new methodology allowing for optimization of the radial and vertical geometry of stellar emissivity and dust opacity, as deduced from the highly resolved emission seen from the vantage point of the Sun. As such, this is the first self-consistent model of the broad-band continuum emission from the MW. In this paper, we present model predictions for the spatially integrated SED of the MW as seen from the Sun, showing good agreement with the data, and give a detailed description of the solutions for the distribution of ISRFs, as well as their physical origin, throughout the volume of the galaxy. We explore how the spatial and spectral distributions of our new predictions for the ISRF in the MW affects the amplitude and spectral distributions of the gamma rays produced via inverse Compton scattering for cosmic ray (CR) electrons situated at different positions in the galaxy, as well as the attenuation of the gamma rays due to interactions of the gamma-ray photons with photons of the ISRF. We also compare and contrast our solutions for the ISRF with those incorporated in the GALPROP package used for modelling the high-energy emission from CR in the MW.