  In November 2019, eROSITA on board of SRG observatory started to map the
entire sky in X-rays. After the 4-year survey program, it will reach flux
limits about 25 times deeper than ROSAT. During the SRG Performance
Verification phase, eROSITA observed a contiguous 140 deg$^2$ area of the sky
down to the final depth of the eROSITA all-sky survey ("eROSITA Final
Equatorial-Depth Survey": eFEDS), with the goal of obtaining a census of the
X-ray emitting populations (stars, compact objects, galaxies, clusters of
galaxies, AGN) that will be discovered over the entire sky.
  This paper presents the identification of the counterparts to the
point-sources detected in eFEDS in the Main and Hard samples described in
Brunner et al 2021, and their multi-wavelength properties, including redshift.
For the identification of the counterparts we combined the results from two
independent methods (NWAY and ASTROMATCH), trained on the multi-wavelength
properties of a sample of 23k XMM-Newton sources detected in the DESI Legacy
Imaging Survey DR8. Then spectroscopic redshifts and photometry from ancillary
surveys are collated for the computation of photometric redshifts. The eFEDS
sources with a reliable counterparts are 24774/27369 (90.5\%) in the Main
sample and 231/246 (93.9\%) in the Hard sample, including 2514 (3) sources for
which a second counterpart is equally likely. [abridged] This paper is
accompanying the eROSITA early data release of all the observations performed
during the performance and verification phase. Together with the catalogs of
primary and secondary counterparts to the Main and Hard samples of the eFEDS
survey this paper releases their multi-wavelength properties and redshifts.
