The use and abuse of nicotine and alcohol account for >100 million disability-adjusted life years across the globe, constituting one of the world’s leading public health problems. Despite this, the majority of genome-wide association studies thus far have been restricted to individuals of European ancestry, representing <1% of known worldwide genetic variation. Here, we leveraged a trans-ancestry GWAS of nicotine and alcohol use in up to 3.4 million individuals from 60 studies with recent ancestry from Africa (N=119,589), America (N=286,026), East Asia (N=296,438), and Europe (N=2,669,029). Overall, we identified 2,143 loci and 3,823 independent variants associated with our five substance use phenotypes: smoking initiation, age of initiation of regular smoking, cigarettes per day, smoking cessation, and alcoholic drinks per week. The trans-ancestry meta-analysis method allows for quantifying the extent to which associated variants differ in effect size by ancestry along four dimensions estimated from multi-dimensional scaling (MDS) of allele frequencies from each participating study. We found that 79.3% (N = 3,032) of independent variants did not differ in magnitude of effect sizes by ancestry. Of the remaining 791 variants, 136 (3.6% of all independent variants) showed strong evidence for allelic heterogeneity indicating that the effect sizes of these variants differ as a function of at least one axis of genetic variation. A single missense variant in the alcohol dehydrogenase gene ADH1B known to be protective against alcohol consumption showed effect size differences on three axes of ancestry variation. An increase on any of these three MDS components was associated with a reduced effect size of the protective allele, on average. Overall, we found that variants associated with alcohol and tobacco use have largely the same effects across population. This is consistent with the idea that the underlying genetic architecture of alcohol and tobacco use is similar across ancestry and informs our understanding of the reasons for reduced portability of polygenic risk scores across populations. While GWAS identified variants are not necessarily causal themselves, these results suggest that the generally low predictive accuracy of scores across populations that has been widely observed may be largely due to reasons other than difference in causal effect sizes, potentially highlighting the importance of differences in linkage disequilibrium patterns and allele frequencies.