We have exploited the Hubble Space Telescope (HST) Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS) J and H-band Wide Field Camera 3 (WFC3)/infrared (IR) imaging to study the properties of (sub-)millimetre galaxies within the Great Observatories Origins Deep Survey South (GOODS-South) field. After using the deep radio (Very Large Array 1.4 GHz) and Spitzer (Infrared Array Camera 8 μm) imaging to identify galaxy counterparts for the (sub-)millimetre sources, we have then utilized the new CANDELS WFC3/IR imaging in two ways. First, the addition of new deep near-IR photometry from both HST and (at K band) the VLT to the existing GOODS-South data base has enabled us to derive improved photometric redshifts and stellar masses, confirming that the (sub-)millimetre sources are massive (〈M 〉 = 2.2 × 1011 ± 0.2 M) galaxies at z 1-3. Secondly, we have exploited the depth and resolution of the WFC3/IR imaging to determine the sizes and morphologies of the galaxies at rest-frame optical wavelengths λrest > 4000 Å. Specifically, we have fitted two-dimensional axisymmetric galaxy models to the WFC3/IR images, varying luminosity, axial ratio, half-light radius r 1/2 and Sérsic index n. Crucially, the wavelength and depth of the WFC3/IR imaging enables modelling of the mass-dominant galaxy, rather than the blue high surface-brightness features which often dominate optical (rest-frame ultraviolet) images of (sub-)millimetre galaxies, and can confuse visual morphological classification. As a result of this analysis, we find that >95 per cent of the rest-frame optical light in almost all of the (sub-)millimetre galaxies is well described by either a single exponential disc (n 1), or a multiple-component system in which the dominant constituent is disc like. We demonstrate that this conclusion is completely consistent with the results of recent high-quality ground-based K-band imaging sampling even longer rest-frame wavelengths, and explain why it is so. These massive disc galaxies are reasonably extended (〈r 1/2〉 = 4.5 ± 0.5 kpc; median r 1/2 = 4.0 kpc), consistent with the sizes of other massive star-forming discs at z 2. In many cases, we find evidence of blue clumps within the sources, with the mass-dominant disc component becoming more significant at longer wavelengths. Finally, only a minority of the sources show evidence for a major galaxy-galaxy interaction. Taken together, these results support the view that most (sub-)millimetre galaxies at z 2 are simply the most extreme examples of normal star-forming galaxies at that era. Interestingly, the only two bulge-dominated galaxies are also the two lowest redshift sources in the sample (z 1), a result which may reflect the structural evolution of high-mass galaxies in general.