An amplitude analysis of the B0→K∗0μ+μ- decay is presented using a dataset corresponding to an integrated luminosity of 4.7 fb-1 of pp collision data collected with the LHCb experiment. For the first time, the coefficients associated to short-distance physics effects, sensitive to processes beyond the standard model, are extracted directly from the data through a q2-unbinned amplitude analysis, where q2 is the μ+μ- invariant mass squared. Long-distance contributions, which originate from nonfactorizable QCD processes, are systematically investigated, and the most accurate assessment to date of their impact on the physical observables is obtained. The pattern of measured corrections to the short-distance couplings is found to be consistent with previous analyses of b- to s-quark transitions, with the largest discrepancy from the standard model predictions found to be at the level of 1.8 standard deviations. The global significance of the observed differences in the decay is 1.4 standard deviations.