  We have obtained mosaic images of NGC 6822 in V and I bands on 77 nights.
  From these data, we have conducted an extensive search for Cepheid variables
over the entire field of the galaxy, and we have found 116 such variables with
periods ranging from 1.7 to 124 days. We used the long-period ($>$ 5.6 days)
Cepheids to establish the period-luminosity relations in V, I and in the
reddening-independent Wesenheit index, which are all very tightly defined.
Fitting the OGLE LMC slopes in the various bands to our data, we have derived
distance values for NGC 6822 in V, I and ${\rm W}_{\rm I}$ which agree very
well among themselves. Our adopted best distance value from the reddening-free
Wesenheit index is 23.34 $\pm$ 0.04 (statistical) $\pm$ 0.05 (systematic) mag.
This value agrees within the combined 1 sigma uncertainties with a previous
distance value derived for NGC 6822 by McAlary et al. from near-IR photometry
of 9 Cepheids, but our new value is significantly more accurate. We compare the
slopes of the Cepheid PL relation in V and I as determined in the five
best-observed nearby galaxies, which span a metallicity range from -1.0 to -0.3
dex, and find the data consistent with no metallicity dependence of the PL
relation slope in this range. Comparing the magnitudes of 10-day Cepheids with
the I-band magnitudes of the TRGB in the same set of galaxies, there is no
evidence either for a significant variation of the period-luminosity zero
points in V and I. The available data limit such a zero point variation to less
than 0.03 mag, in the considered low-metallicity regime.
