The selection of low-radioactive construction materials is of utmost importance for the success of low-energy rare event search experiments. Besides radioactive contaminants in the bulk, the emanation of radioactive radon atoms from material surfaces attains increasing relevance in the effort to further reduce the background of such experiments. In this work, we present the $^{222}$Rn emanation measurements performed for the XENON1T dark matter experiment. Together with the bulk impurity screening campaign, the results enabled us to select the radio-purest construction materials, targeting a $^{222}$Rn activity concentration of 10 $mu$Bq/kg in 3.2 t of xenon. The knowledge of the distribution of the $^{222}$Rn sources allowed us to selectively eliminate critical components in the course of the experiment. The predictions from the emanation measurements were compared to data of the $^{222}$Rn activity concentration in XENON1T. The final $^{222}$Rn activity concentration of (4.5 $pm$ 0.1) $mu$Bq/kg in the target of XENON1T is the lowest ever achieved in a xenon dark matter experiment.
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