Using the data samples of 1.31×109 J/ψ events and 4.48×108 ψ(3686) events collected with the BESIII detector, partial wave analyses on the decays J/ψ and ψ(3686)→π+π-η′ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be J/ψ and ψ(3686) decays to ρη′. In the J/ψ decay, the branching fraction B(J/ψ→ρη′) is determined to be (7.90±0.19(stat)±0.49(sys))×10-5. Two solutions are found in the ψ(3686) decay, and the corresponding branching fraction B(ψ(3686)→ρη′) is (1.02±0.11(stat)±0.24(sys))×10-5 for the case of destructive interference, and (5.69±1.28(stat)±2.36(sys))×10-6 for constructive interference. As a consequence, the ratios of branching fractions between ψ(3686) and J/ψ decays to ρη′ are calculated to be (12.9±1.4(stat)±3.1(sys))% and (7.2±1.6(stat)±3.0(sys))%, respectively. We also determine the inclusive branching fractions of J/ψ and ψ(3686) decays to π+π-η′ to be (1.36±0.02(stat)±0.08(sys))×10-4 and (1.51±0.14(stat)±0.23(sys))×10-5, respectively.