The observation of replica bands by angle-resolved photoemission spectroscopy has ignited interest in the study of electron-phonon coupling at low carrier densities, particularly in monolayer FeSe/SrTiO3, where the appearance of replica bands has motivated theoretical work suggesting that the interfacial coupling of electrons in the FeSe layer to optical phonons in the SrTiO3 substrate might contribute to the enhanced superconducting pairing temperature. Alternatively, it has also been recently proposed that such replica bands might instead originate from extrinsic final state losses associated with the photoemission process. Here, we perform a quantitative examination of replica bands in monolayer FeSe/SrTiO3, where we are able to conclusively demonstrate that the replica bands are indeed signatures of intrinsic electron-boson coupling, and not associated with final state effects. A detailed analysis of the energy splittings and relative peak intensities between the higher-order replicas, as well as other self-energy effects, allows us to determine that the interfacial electron-phonon coupling in the system corresponds to a value of λ=0.19±0.02, providing valuable insights into the enhancement of superconductivity in monolayer FeSe/SrTiO3. The methodology employed here can also serve as a new and general approach for making more rigorous and quantitative comparisons to theoretical calculations of electron-phonon interactions and coupling constants. © 2021 American Physical Society.