A direct and complete measurement of isotopic fission-fragment yields of ^{239}U has been performed for the first time. The ^{239}U fissioning system was produced with an average excitation energy of 8.3 MeV in one-neutron transfer reactions between a ^{238}U beam and a ^{9}Be target at Coulomb barrier energies. The fission fragments were detected and isotopically identified using the VAMOS++ spectrometer at the GANIL facility. The measurement allows us to directly evaluate the fission models at excitation energies of fast neutrons, which are relevant for next-generation nuclear reactors. The present data, in agreement with model calculations, do not support the recently reported anomaly in the fission-fragment yields of ^{239}U, and they confirm the persistence of spherical shell effects in the Sn region at excitation energies exceeding the fission barrier by a few mega-electron volts.