The background radiations in the optical and the infrared constitute a relevant cause of energy loss in the propagation of high energy particles through space. In particular, TeV observations with Cherenkov telescopes of extragalactic sources are influenced by the opacity effects due to the interaction of the very high-energy source photons with the background light. With the aim of assessing with the best possible detail these opacity terms, we have modelled the extragalactic optical and IR backgrounds using available information on cosmic sources in the universe from far-UV to sub-mm wavelengths over a wide range of cosmic epochs. We have exploited the relevant cosmological survey data - including number counts, redshift distributions, luminosity functions - from ground-based observatories in the optical, near-IR, and sub-mm, as well as multi-wavelength information coming from space telescopes, HST, ISO and Spitzer. Additional constraints have been used from direct measurements or upper limits on the extragalactic backgrounds by dedicated missions (COBE). All data were fitted and interpolated with a multi-wavelength backward evolutionary model, allowing us to estimate the background photon density and its redshift evolution. From the redshift-dependent background spectrum, the photon-photon opacities for sources of high-energy emission at any redshifts were then computed. The same results can also be used to compute the optical depths for any kind of processes in the intergalactic space involving interactions with background photons (like scattering of cosmic-ray particles). We have applied our photon-photon opacity estimates to the analysis of spectral data at TeV energies on a few BLAZARs of particular interest. [abridged]