We exploit the deepest existing far-infrared (FIR) data obtained so far by Herschel at 100 and 160 um in the GOODS-N, as part of the PACS Evolutionary Probe (PEP) survey, to derive for the first time the evolution of the rest-frame 60-um, 90-um, and total IR luminosity functions (LFs) of galaxies and AGNs from z=0 to unprecedented high redshifts (z~2-3). The PEP LFs were computed using the 1/Vmax method. The FIR sources were classified by means of a detailed broad- band SED-fitting analysis and spectral characterisation. Based on the best-fit model results, k-correction and total IR (8-1000 um) luminosity were obtained for each source. LFs (monochromatic and total) were then derived for various IR populations separately in different redshift bins and compared to backward evolution model predictions. We detect strong evolution in the LF to at least z~2. Objects with SEDs similar to local spiral galaxies are the major contributors to the star formation density (SFD) at z< 0.3, then, as redshift increases, moderate SF galaxies - most likely containing a low-luminosity AGN - start dominating up to z ~= 1.5. At >1.5 the SFD is dominated by the contributions of starburst galaxies. In agreement with previous findings, the comoving IR LD derived from our data evolves approximately as (1 + z)^(3.8+/-0.3) up to z~1, there being some evidence of flattening up to z~2. Comment: Accepted for publication in the A&A Herschel first results Special Issue