Within the framework of the generalized QCD factorization formalism, we perform the first global analysis of the jet transport coefficient ($\hat q$) for cold nuclear matter. The analysis takes into account the world data on transverse momentum broadening in semi-inclusive electron-nucleus deep inelastic scattering, Drell-Yan dilepton and heavy quarkonium production in proton-nucleus collisions, as well as the nuclear modification of the structure functions in deep inelastic scattering, comprising a total of 215 data points from 8 data sets. For the first time, we clarify quantitatively the universality and probing scale dependence of the nuclear medium property as encoded in $\hat q$. We expect that the determined parametrization of $\hat q$ in cold nuclear matter will have significant impact on precise identification of the transport property of hot dense medium created in heavy ion collisions.