We calculate the colours and luminosities of redshift z = 0.1 galaxies from the EAGLE simulation suite using the GALAXEV population synthesis models. We take into account obscuration by dust in birth clouds and diffuse interstellar medium using a two-component screen model, following the prescription of Charlot and Fall. We compare models in which the dust optical depth is constant to models where it depends on gas metallicity, gas fraction and orientation. The colours of EAGLE galaxies for the more sophisticated models are in broad agreement with those of observed galaxies. In particular, EAGLE produces a red sequence of passive galaxies and a blue cloud of star-forming galaxies, with approximately the correct fraction of galaxies in each population and with g - r colours within 0.1 mag of those observed. Luminosity functions from ultraviolet to near-infrared wavelengths differ from observations at a level comparable to systematic shifts resulting from a choice between Petrosian and Kron photometric apertures. Despite the generally good agreement there are clear discrepancies with observations. The blue cloud of EAGLE galaxies extends to somewhat higher luminosities than in the data, consistent with the modest underestimate of the passive fraction in massive EAGLE galaxies. There is also a moderate excess of bright blue galaxies compared to observations. The overall level of agreement with the observed colour distribution suggests that EAGLE galaxies at z = 0.1 have ages, metallicities and levels of obscuration that are comparable to those of observed galaxies.