Transmission eigenchannels are building blocks of coherent wave transport in diffusive media, and selective excitation of individual eigenchannels can lead to diverse transport behaviour. An essential yet poorly understood property is the transverse spatial profile of each eigenchannel, which is relevant for the associated energy density and critical for coupling light into and out of it. Here, we discover that the transmission eigenchannels of a disordered slab possess exponentially localized incident and outgoing profiles, even in the diffusive regime far from Anderson localization. Such transverse localization arises from a combination of reciprocity, local coupling of spatial modes and non-local correlations of scattered waves. Experimentally, we observe signatures of such localization even with finite illumination area. The transverse localization of high-transmission channels enhances optical energy densities inside turbid media, which will be important for light—matter interactions and imaging applications.