Using a sample of 1.3×109J/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.)]×10-5 and B(η′→π+π-π0π0)= [1.82±0.35(stat.)±0.18(syst.)]×10-4, which are consistent with theoretical predictions based on a combination of chiral perturbation theory and vector-meson dominance.