Most transcriptome-wide association studies (TWASs) so far focus on European ancestry and lack diversity. To overcome this limitation, we aggregated genome-wide association study (GWAS) summary statistics, whole-genome sequences and expression quantitative trait locus (eQTL) data from diverse ancestries. We developed a new approach, TESLA (multi-ancestry integrative study using an optimal linear combination of association statistics), to integrate an eQTL dataset with a multi-ancestry GWAS. By exploiting shared phenotypic effects between ancestries and accommodating potential effect heterogeneities, TESLA improves power over other TWAS methods. When applied to tobacco use phenotypes, TESLA identified 273 new genes, up to 55% more compared with alternative TWAS methods. These hits and subsequent fine mapping using TESLA point to target genes with biological relevance. In silico drug-repurposing analyses highlight several drugs with known efficacy, including dextromethorphan and galantamine, and new drugs such as muscle relaxants that may be repurposed for treating nicotine addiction.