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 Soszyński , Gieren and Pietrzyński , 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 \pm 0.021 ( random error ) mag , with an additional systematic uncertainty of \sim 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 \pm 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 & 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 .