We perform the first global fit to inclusive B→Xsγ measurements using a model-independent treatment of the nonperturbative b-quark distribution function, with next-to-next-to-leading logarithmic resummation and O(α2s) fixed-order contributions. The normalization of the B→Xsγ decay rate, given by |Cincl7VtbV∗ts|2, is sensitive to physics beyond the standard model (SM). We determine |Cincl7VtbV∗ts|=(14.77±0.51fit±0.59theory±0.08param)×10−3, in good agreement with the SM prediction, and the b-quark mass m1Sb=(4.750±0.027fit±0.033theory±0.003param) GeV. Our results suggest that the uncertainties in the extracted B→Xsγ rate have been underestimated by up to a factor of 2, leaving more room for beyond-SM contributions.