Tobacco smoke, alone or combined with alcohol, is the predominant cause of head and neck cancer (HNC). Here, we further explore how tobacco exposure contributes to cancer development by mutational signature analysis of 265 whole-genome sequenced HNC from eight countries. Six tobacco-associated mutational signatures were detected, including some not previously reported. Differences in HNC incidence between countries corresponded with differences in mutation burdens of tobacco-associated signatures, consistent with the dominant role of tobacco in HNC causation. Differences were found in the burden of tobacco-associated signatures between anatomical subsites, suggesting that tissue-specific factors modulate mutagenesis. We identified an association between tobacco smoking and three additional alcohol-related signatures indicating synergism between the two exposures. Tobacco smoking was associated with differences in the mutational spectra and repertoire of driver mutations in cancer genes, and in patterns of copy number change. Together, the results demonstrate the multiple pathways by which tobacco smoke can influence the evolution of cancer cell clones.