By exploiting the VLA-COSMOS and the Herschel-PEP surveys, we investigate the Far Infrared (FIR) properties of radio-selected AGN. To this purpose, from VLA-COSMOS we considered the 1537, F[1.4 GHz]>0.06 mJy sources with a reliable redshift estimate, and sub-divided them into star-forming galaxies and AGN solely on the basis of their radio luminosity. The AGN sample is complete with respect to radio selection at all z<~3.5. 832 radio sources have a counterpart in the PEP catalogue. 175 are AGN. Their redshift distribution closely resembles that of the total radio-selected AGN population, and exhibits two marked peaks at z~0.9 and z~2.5. We find that the probability for a radio-selected AGN to be detected at FIR wavelengths is both a function of radio power and redshift, whereby powerful sources are more likely to be FIR emitters at earlier epochs. This is due to two distinct effects: 1) at all radio luminosities, FIR activity monotonically increases with look-back time and 2) radio activity of AGN origin is increasingly less effective at inhibiting FIR emission. Radio-selected AGN with FIR emission are preferentially located in galaxies which are smaller than those hosting FIR-inactive sources. Furthermore, at all z<~2, there seems to be a preferential (stellar) mass scale M ~[10^{10}-10^{11}] Msun which maximizes the chances for FIR emission. We find such FIR (and MIR) emission to be due to processes indistinguishable from those which power star-forming galaxies. It follows that radio emission in at least 35% of the entire AGN population is the sum of two contributions: AGN accretion and star-forming processes within the host galaxy.
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