We perform the first global fit to inclusive $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ measurements using a model-independent treatment of the nonperturbative $b$-quark distribution function, with next-to-next-to-leading logarithmic resummation and $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})$ fixed-order contributions. The normalization of the $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ decay rate, given by $|{C}_{7}^{\mathrm{incl}}{V}_{tb}{V}_{ts}^{*}{|}^{2}$, is sensitive to physics beyond the standard model (SM). We determine $|{C}_{7}^{\mathrm{incl}}{V}_{tb}{V}_{ts}^{*}|=(14.77\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.5{1}_{\mathrm{fit}}\ifmmode\pm\else\textpm\fi{}0.5{9}_{\text{theory}}\ifmmode\pm\else\textpm\fi{}0.0{8}_{\text{param}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, in good agreement with the SM prediction, and the $b$-quark mass ${m}_{b}^{1S}=(4.750\ifmmode\pm\else\textpm\fi{}0.02{7}_{\mathrm{fit}}\ifmmode\pm\else\textpm\fi{}0.03{3}_{\text{theory}}\ifmmode\pm\else\textpm\fi{}0.00{3}_{\text{param}})\text{ }\text{ }\mathrm{GeV}$. Our results suggest that the uncertainties in the extracted $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ rate have been underestimated by up to a factor of 2, leaving more room for beyond-SM contributions.