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Abstract Assuming Galactic cosmic rays originate in supernovae and the winds of massive stars, starburst galaxies should produce very-high-energy (VHE;E > 100 GeV) gamma-ray emission via the interaction of their copious quantities of cosmic rays with the large reservoirs of dense gas within the galaxies. Such VHE emission was detected by VERITAS from the starburst galaxy M82 in 2008–09. An extensive, multiyear campaign followed these initial observations, yielding a total of 254 hr of good-quality VERITAS data on M82. Leveraging modern analysis techniques and the larger exposure, these VERITAS data show a more statistically significant VHE signal (∼6.5 standard deviations,σ). The corresponding photon spectrum is well fit by a power law (Γ = 2.3 ± 0.3_stat ± 0.2_sys), and the observed integral flux isF(>450 GeV) = (3.2 ± 0.6_stat ± 0.6_sys) × 10⁻¹³cm⁻²s⁻¹, or ∼0.4% of the Crab Nebula flux above the same energy threshold. The improved VERITAS measurements, when combined with various multiwavelength data, enable modeling of the underlying emission and transport processes. A purely leptonic scenario is found to be a poor representation of the gamma-ray spectral energy distribution (SED). A lepto-hadronic scenario with cosmic rays following a power-law spectrum in momentum (indexs ≃ 2.25) and with significant bremsstrahlung below 1 GeV provides a good match to the observed SED. The synchrotron emission from the secondary electrons indicates that efficient nonradiative losses of cosmic-ray electrons may be related to advective escape from the starburst core.