Snake envenomation is a neglected tropical disease, with 600 species causing over 100,000 deaths and 300,000 permanent disabilities in humans annually. Broadly neutralizing antibodies and broad chemical inhibitors have been proposed as solutions, but how to develop a therapeutically effective cocktail and the number of required components have been unclear. To address this gap, we iteratively recovered two broadly neutralizing antivenom antibodies from the memory B cells of a hyperimmune human donor with extensive snake venom exposure. The antibodies recognized conserved neutralizing epitopes on prevalent long and short snake neurotoxins, with crystal structures revealing antibody mimicry of the interfaces between these neurotoxins and their host target, the nicotinic acetylcholine receptor. We combined and tested these antibodies and the phospholipase inhibitor varespladib. A 3-component cocktail rescued animals from whole-venom challenge of all species in a 19-member WHO Category 1 and Category 2 elapid diversity set, with complete protection against most snakes observed.