This paper is the fourth in a series reporting the results of the ATESP rad
io survey, which was made at 1.4 GHz with the Australia Telescope Compact A
rray. The survey consists of 16 radio mosaics with similar to8 " x 14 " res
olution and uniform sensitivity (1 sigma noise level similar to 79 mu Jy) o
ver the region covered by the ESO Slice Project redshift survey (similar to
26 sq deg at delta similar to -40 degrees). The ATESP survey has produced
a catalogue of 2967 radio sources down to a flux limit of similar to0.5 mJy
(6 sigma). In this paper we present the optical identifications over a 3 s
q deg region coinciding with the Patch A of the public E;SO Imaging Survey
(EIS). In this region deep photometry and 95% complete object catalogues in
the I band are available down to I similar to 22.5. These data allowed us
to identify 219 of the 386 ATESP sources present in the region. This corres
ponds to an identification rate of similar to 57% For a magnitude-limited s
ample of 70 optically identified sources with I < 19.0 we have obtained com
plete and good quality spectroscopic data at the ESO 3.6 m telescope at La
Silla. This data allow ed us to determine redshift measurements and reliabl
e spectroscopic classification for all sources (except one). From the analy
sis of the spectroscopic sample we find that the composition of the faint r
adio source population abruptly changes going from mJy to sub-mJy fluxes: t
he early-type galaxies largely dominate the mJy population (60%), while sta
r forming processes become important in the sub-mJy regime. Starburst and p
ost-starburst galaxies go from 13% at S greater than or equal to 1 mJy to 3
9% at S < 1 mJy. Nevertheless, at sub-mJy fluxes, early-ype galaxies still
constitute a significant fraction (25%) of the whole population. Furthermor
e we show that. due to the distribution of radio-to-optical ratios, sub-mJy
samples with fainter spectroscopic follow-ups should be increasingly sensi
tive to the population of early-type galaxies, while a larger fraction of s
tar-forming galaxies would be expected in mu Jy samples. We compare our res
ults with others obtained from studies of sub-mJy samples and we show how t
he existing discrepancies can be explained in terms of selection affects.