[en] We report branching fraction measurements of the decays B⁺ → ηℓ⁺νℓ and B⁺ → η'ℓ⁺νℓ based on 711 fb^–1 of data collected near the Υ(4S) resonance with the Belle experiment at the KEKB asymmetric-energy e⁺e^– collider. This data sample contains 772 million BB¯ events. One of the two B mesons is fully reconstructed in a hadronic decay mode. Among the remaining (“signal-B”) daughters, we search for the η meson in two decay channels, η → γγ and η → π⁺π^–π⁰, and reconstruct the η' meson in η' → ηπ⁺π^– with subsequent decay of the η into γγ. Combining the two η modes and using an extended maximum likelihood, the B⁺ → ηℓ⁺νℓ branching fraction is measured to be (4.2 ± 1.1(stat.) ± 0.3(syst.)) × 10^–5. For B⁺ → η'ℓ⁺νℓ, we observe no significant signal and set an upper limit of 0.72 × 10^–4 at 90% confidence level.