We present the first global extraction of the jet transport coefficient (qˆ) for cold nuclear matter within the framework of higher-twist expansion. The analysis takes into account the world data on transverse momentum broadening in semi-inclusive e-A deep inelastic scattering (DIS) and in Drell-Yan dilepton and heavy quarkonium production in p-A collisions, as well as the nuclear modification of the structure functions in DIS. The results of this work provide the first quantitative evidence for the universality and non-trivial scale dependence of the medium transport property, similar to that for nucleon structure as encoded in the standard parton distribution functions. We expect the extracted scale dependence of qˆ for cold nuclear matter can be extended to precisely identify the fundamental property of quark gluon plasma.