Bread wheat expanded its habitat from a core area of the Fertile Crescent to global environments within ~10,000 years. The genetic mechanisms of this remarkable evolutionary success are not well understood. By whole-genome sequencing of populations from 25 subspecies within the genera Triticum and Aegilops, we identified composite introgression from wild populations contributing to a substantial portion (4-32%) of the bread wheat genome, which increased the genetic diversity of bread wheat and allowed its divergent adaptation. Meanwhile, convergent adaptation to human selection showed 2- to 16-fold enrichment relative to random expectation-a certain set of genes were repeatedly selected in Triticum species despite their drastic differences in ploidy levels and growing zones, indicating the important role of evolutionary constraints in shaping the adaptive landscape of bread wheat. These results showed the genetic necessities of wheat as a global crop and provided new perspectives on transferring adaptive success across species for crop improvement.