We report branching fraction measurements of the decays $B^+toetaell^+ u_ell$ and $B^+toeta^primeell^+ u_ell$ based on 711~fb$^{-1}$ of data collected near the $Upsilon(4S)$ resonance with the Belle experiment at the KEKB asymmetric-energy $e^+e^-$ collider. This data sample contains 772 million $Bbar B$~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 $eta$~meson in two decay channels, $etatogammagamma$ and $etatopi^+pi^-pi^0$, and reconstruct the $eta^{prime}$~meson in $eta^primetoetapi^+pi^-$ with subsequent decay of the $eta$ into $gammagamma$. Combining the two $eta$ modes and using an extended maximum likelihood, the $B^+toetaell^+ u_ell$ branching fraction is measured to be $(4.2pm 1.1 (rm stat.)pm 0.3 (rm syst.))times 10^{-5}$. For $B^+toeta^primeell^+ u_ell$, we observe no significant signal and set an upper limit of $0.72times 10^{-4}$ at 90% confidence level.