For the first time an analysis of all experimental data on the differential cross section of elastic γp scattering at photon energies ω < 150 MeV is performed in order to determine the electric (α p ) and magnetic (β p ) polarizabilities of the proton. A fit of these data with the two free parameters, α p and β p , embedded into a theoretical cross section obtained on the basis of finite-energy s-channel dispersion relations gives the following world-average values of the proton polarizabilities (in units of 10 −4 fm 3 ): α exp p = 11.7 ± 0.8 (stat. + sys.) ± 0.7 (model), β exp p = 2.3 ± 0.9 (stat. + sys.) ± 0.7 (model), where the first error takes into account statistical and systematic errors of the experimental cross sections and the second error does model uncertainties in the theoretical cross section.