We have exploited the HST CANDELS WFC3/IR imaging to study the properties of (sub-)mm galaxies in GOODS-South. After using the deep radio and Spitzer imaging to identify galaxy counterparts for the (sub-)mm sources, we have used the new CANDELS data in two ways. First, we have derived improved photometric redshifts and stellar masses, confirming that the (sub-)mm galaxies are massive (<M*>=2.2x10^11 M_solar) galaxies at z=1-3. Second, 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, fitting two-dimensional axi-symmetric Sersic models. Crucially, the WFC3/IR H-band imaging enables modelling of the mass-dominant galaxy, rather than the blue high-surface brightness features which often dominate optical (rest-frame UV) images of (sub-)mm galaxies, and can confuse visual morphological classification. As a result of this analysis we find that >95% of the rest-frame optical light in almost all of the (sub-)mm galaxies is well-described by either a single exponential disk, or a multiple-component system in which the dominant constituent is disk-like. We demonstrate that this conclusion is consistent with the results of high-quality ground-based K-band imaging, and explain why. The massive disk galaxies which host luminous (sub-)mm emission are reasonably extended (r_e=4 kpc), consistent with the sizes of other massive star-forming disks at z~2. In many cases we find evidence of blue clumps within the sources, with the mass-dominant disk 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-)mm galaxies at z~2 are simply the most extreme examples of normal star-forming galaxies at that era.