Transverse Anderson localization of light allows localized optical-beam-transport through a transversely disordered and longitudinally invariant medium. Its successful implementation in disordered optical fibres recently resulted in the propagation of localized beams of radii comparable to that of conventional optical fibres. Here we demonstrate optical image transport using transverse Anderson localization of light. The image transport quality obtained in the polymer disordered optical fibre is comparable to or better than some of the best commercially available multicore image fibres with less pixelation and higher contrast. It is argued that considerable improvement in image transport quality can be obtained in a disordered fibre made from a glass matrix with near wavelength-size randomly distributed air-holes with an air-hole fill-fraction of 50%. Our results open the way to device-level implementation of the transverse Anderson localization of light with potential applications in biological and medical imaging.