The Siluro-Devonian adaptive radiation of jawed vertebrates, which underpins almost all living vertebrate biodiversity, is characterized by the evolutionary innovation of the lower jaw. Multiple lines of evidence have suggested that the jaw evolved from a rostral gill arch, but when the jaw took on a feeding function remains unclear. We quantified the variety of form in the earliest jaws in the fossil record from which we generated a theoretical morphospace that we then tested for functional optimality. By drawing comparisons with the real jaw data and reconstructed jaw morphologies from phylogenetically inferred ancestors, our results show that the earliest jaw shapes were optimized for fast closure and stress resistance, inferring a predatory feeding function. Jaw shapes became less optimal for these functions during the later radiation of jawed vertebrates. Thus, the evolution of jaw morphology has continually explored previously unoccupied morphospace and accumulated disparity through time, laying the foundation for diverse feeding strategies and the success of jawed vertebrates.