Using a sample of 1.3 x 10⁹ J/ψ events collected with the BESIII detector, we report the first observation of η'→π⁺π⁻π⁺π⁻ and η'→π⁺π⁻π⁰π⁰. The measured branching fractions are ℬ(η'→π⁺π⁻π⁺π⁻) = [8.53 ± 0.69(stat.) ± 0.64(syst.)] x 10⁻⁵ and ℬ(η'→π⁺π⁻π⁰π⁰) = [1.82 ± 0.35(stat.) ± 0.18(syst.)] x 10⁻⁴, which are consistent with theoretical predictions based on a combination of chiral perturbation theory and vector-meson dominance.