We measure the complete set of angular coefficients J_{i} for exclusive B[over ¯]→D^{*}ℓν[over ¯]_{ℓ} decays (ℓ=e, μ). Our analysis uses the full 711 fb^{-1} Belle dataset with hadronic tag-side reconstruction. The results allow us to extract the form factors describing the B[over ¯]→D^{*} transition and the Cabibbo-Kobayashi-Maskawa matrix element |V_{cb}|. Using recent lattice QCD calculations for the hadronic form factors, we find |V_{cb}|=(40.7±0.7)×10^{-3} using the Boyd-Grinstein-Lebed parametrization, compatible with determinations from inclusive semileptonic decays. We search for lepton flavor universality violation as a function of the hadronic recoil parameter w and investigate the differences of the electron and muon angular distributions. We find no deviation from standard model expectations.