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Abstract The detection of the hyper-bright gamma-ray burst (GRB) 221009A enables us to explore the nature of the GRB emission and the origin of very high-energy gamma rays. We analyze the Fermi Large Area Telescope (Fermi-LAT) data of this burst and investigate the GeV–TeV emission in the framework of the external reverse-shock model. We show that the early ∼1–10 GeV emission can be explained by the external inverse-Compton mechanism via upscattering MeV gamma rays by electrons accelerated at the reverse shock, in addition to the synchrotron self-Compton component. The predicted early optical flux could have been brighter than that of the naked-eye GRB 080319B. We also show that proton synchrotron emission from accelerated ultrahigh-energy cosmic rays (UHECRs) is detectable and could potentially explain ≳TeV photons detected by LHAASO or constrain the UHECR acceleration mechanism. Our model suggests that the detection of $\mathit{}\left(10\mathrm{TeV}\right)$photons with energies up to ∼18 TeV is possible for reasonable models of the extragalactic background light without invoking new physics and predicts anticorrelations between MeV photons and TeV photons, which can be tested with the LHAASO data.