MAXI J1659−152 was discovered on 2010 September 25 as a new X-ray transient, initially identified as a gamma-ray burst, but was later shown to be a new X-ray binary with a black hole as the most likely compact object. Dips in the X-ray light curves have revealed that MAXI J1659−152 is the shortest period black hole candidate identified to date. Here we present the results of a large observing campaign at radio, submillimetre, near-infrared (nIR), optical and ultraviolet (UV) wavelengths. We have combined this very rich data set with the available X-ray observations to compile a broad-band picture of the evolution of this outburst. We have performed broad-band spectral modelling, demonstrating the presence of a spectral break at radio frequencies and a relationship between the radio spectrum and X-ray states. Also, we have determined physical parameters of the accretion disc and put them into context with respect to the other parameters of the binary system. Finally, we have investigated the radio-X-ray and nIR/optical/UV-X-ray correlations up to ∼3 yr after the outburst onset to examine the link between the jet and the accretion disc, and found that there is no significant jet contribution to the nIR emission when the source is in the soft or intermediate X-ray spectral state, consistent with our detection of the jet break at radio frequencies during these states.