  We have obtained deep images in the near-infrared J and K filters of four
fields in the Sculptor Group spiral galaxy NGC 55 with the ESO VLT and ISAAC
camera. For 40 long-period Cepheid variables in these fields which were
recently discovered by Pietrzy{\'n}ski et al., we have determined mean J and K
magnitudes from observations at two epochs, and derived distance moduli from
the observed PL relations in these bands. Using these values together with the
previously measured distance moduli in the optical V and I bands, we have
determined a total mean reddening of the NGC 55 Cepheids of E(B-V)=0.127 $\pm$
0.019 mag, which is mostly produced inside NGC 55 itself. For the true distance
modulus of the galaxy, our multiwavelength analysis yields a value of 26.434
$\pm$ 0.037 mag (random error), corresponding to a distance of 1.94 $\pm$ 0.03
Mpc. This value is tied to an adopted true LMC distance modulus of 18.50 mag.
The systematic uncertainty of our derived Cepheid distance to NGC 55 (apart
from the uncertainty on the adopted LMC distance) is $\pm$4%, with the main
contribution likely to come from the effect of blending of some of the Cepheids
with unresolved companion stars. The distance of NGC 55 derived from our
multiwavelength Cepheid analysis agrees within the errors with the distance of
NGC 300, strengthening the case for a physical association of these two
Sculptor Group galaxies.
