Solitons are non-dispersing localized waves that occur in diverse physical settings, including liquids, optical fibres, plasmas and condensed matter. They attract interest owing to their particle-like nature and are useful for applications such as in telecommunications. A variety of optical solitons have been observed, but versions that involve both spatial and temporal degrees of freedom are rare. Optical fibres designed to support multiple transverse modes offer opportunities to study wave propagation in a setting that is intermediate between single-mode fibre and free-space propagation. Here we report the observation of optical solitons and soliton self-frequency shifting in graded-index multimode fibre. These wave packets can be modelled as multicomponent solitons, or as solitons of the Gross-Pitaevskii equation. Solitons in graded-index fibres should enable increased data rates in low-cost telecommunications systems, are pertinent to space-division multiplexing, and can offer a new route to mode-area scaling for high-power lasers and transmission.