  We have measured near-infrared magnitudes in the J and K bands for 56 Cepheid
variables in the Local Group galaxy NGC 6822 with well-determined periods and
optical light curves in the V and I bands. Using the template light curve
approach of Soszynski, Gieren and Pietrzynski, accurate mean magnitudes were
obtained from these data which allowed us to determine with unprecedented
accuracy the distance to NGC 6822 from a multi-wavelength period-luminosity
solution in the VIJK bands. From our data, we obtain a distance to NGC 6822 of
(m-M)_{0} = 23.312 +- 0.021 (random error) mag, with an additional systematic
uncertainty of about 3 %. This distance value is tied to an assumed LMC
distance modulus of 18.50. From our multiwavelength approach, we find for the
total (average) reddening to the NGC 6822 Cepheids E(B-V) = 0.356 +- 0.013 mag,
which is in excellent agreement with a previous determination of McGonegal et
al. from near-infrared photometry and implies significant internal reddening of
the Cepheids in NGC 6822. Our present, definitive distance determination of NGC
6822 from Cepheids agrees within 2 % with the previous distance we had derived
from optical photometry alone, but has significantly reduced error bars.
  Our Cepheid distance to NGC 6822 is in excellent agreement with the recent
independent determination of Cioni and Habing from the I-band magnitude of the
tip of the red giant branch. It also agrees well, within the errors, with the
early determination of McGonegal et al. (1983) from random-phase H-band
photometry of nine Cepheids.
