Hendra virus (HeV) and Nipah virus (NiV) are henipaviruses (HNVs) causing respiratory illness and severe encephalitis in humans, with fatality rates of 50-100%. There are no licensed therapeutics or vaccines to protect humans. HeV and NiV use a receptor-binding glycoprotein (G) and a fusion glycoprotein (F) to enter host cells. HNV F and G are the main targets of the humoral immune response, and the presence of neutralizing antibodies is a correlate of protection against NiV and HeV in experimentally infected animals. We describe here two cross-reactive F-specific antibodies, 1F5 and 12B2, that neutralize NiV and HeV through inhibition of membrane fusion. Cryo-electron microscopy structures reveal that 1F5 and 12B2 recognize distinct prefusion-specific, conserved quaternary epitopes and lock F in its prefusion conformation. We provide proof-of-concept for using antibody cocktails for neutralizing NiV and HeV and define a roadmap for developing effective countermeasures against these highly pathogenic viruses.