β decays from heavy, neutron-rich nuclei with A∼190 have been investigated following their production via the relativistic projectile fragmentation of an E/A=1 GeV 208Pb primary beam on a ∼2.5 g/cm2 9Be target. The reaction products were separated and identified using the GSI FRagment Separator (FRS) and stopped in the RISING active stopper. γ decays were observed and correlated with these secondary ions on an event-by-event basis such that γ-ray transitions following from both internal (isomeric) and β decays were recorded. A number of discrete, β-delayed γ-ray transitions associated with β decays from 194Re to excited states in 194Os have been observed, including previously reported decays from the yrast Iπ=(6+) state. Three previously unreported γ-ray transitions with energies 194, 349, and 554 keV are also identified; these transitions are associated with decays from higher spin states in 194Os. The results of these investigations are compared with theoretical predictions from Nilsson multi-quasiparticle (MQP) calculations. Based on lifetime measurements and the observed feeding pattern to states in 194Os, it is concluded that there are three β−-decaying states in 194Re.