Single-photon emitters (SPEs) in hexagonal boron nitride (hBN) have garnered increasing attention over the last few years due to their superior optical properties. However, despite the vast range of experimental results and theoretical calculations, the defect structure responsible for the observed emission has remained elusive. Here, by controlling the incorporation of impurities into hBN via various bottom-up synthesis methods and directly through ion implantation, we provide direct evidence that the visible SPEs are carbon related. Room-temperature optically detected magnetic resonance is demonstrated on ensembles of these defects. We perform ion-implantation experiments and confirm that only carbon implantation creates SPEs in the visible spectral range. Computational analysis of the simplest 12 carbon-containing defect species suggest the negatively charged VBCN- defect as a viable candidate and predict that out-of-plane deformations make the defect environmentally sensitive. Our results resolve a long-standing debate about the origin of single emitters at the visible range in hBN and will be key to the deterministic engineering of these defects for quantum photonic devices.