The atomistic and electronic structures of isolated hydrogen states in BeO were studied by ab initio calculations and muonium spectroscopy (µSR). Whereas standard density-functional theory with a semi-local GGA functional led to a detailed probing of all possible minimum-energy configurations of hydrogen further calculations with the hybrid HSE06 functional provided improved properties avoiding band-gap and self-interaction errors. Similarly to earlier findings for the other wide-gap alkaline-earth oxide, MgO, hydrogen in BeO is also predicted to be an amphoteric defect with the pinning level, E(+/-), positioned in the mid-gap region. Both donor and acceptor levels were found too deep in the gap to allow for hydrogen to act as a source of free carriers. Whereas, hydrogen in its positively-charged state, H⁺, adopts exclusively hydroxide-bond OH configurations, H⁰ and H^- instead show a preference to occupy cage-like interstitial sites in the lattice. H⁰ in particular displays a multitude of minimum-energy configurations: its lowest-energy ground state resembles closely a trapped-atom state with a nearly spherical spin-density profile. In contrast to the strongly ionic MgO, H⁰ in BeO was further found to stabilise in additional higher-energy elongated-bond OH configurations whose existence should be traced to a partial covalent character of the Be-O bonding. Calculations of the proton-electron hyperfine coupling for all H⁰ states showed that the ground-state interstitial H⁰ configuration is dominated by an isotropic hyperfine interaction with a magnitude very close to the vacuum value, a finding corroborated by the µSR-spectroscopy data.