Recent studies based on lattice Monte Carlo simulations of quantum chromodynamics (QCD)-the theory of strong interactions-have demonstrated that at high temperature there is a phase change from confined hadronic matter to a deconfined quark-gluon plasma in which quarks and gluons can travel distances that greatly exceed the size of hadrons. Here we show that the phase structure of such strongly interacting matter can be decoded by analysing particle production in high-energy nuclear collisions within the framework of statistical hadronization, which accounts for the thermal distribution of particle species. Our results represent a phenomenological determination of the location of the phase boundary of strongly interacting matter, and imply quark-hadron duality at this boundary.