Developing insight into tissue-specific transcriptional mechanisms can help improve our understanding of how genetic variants exert their effects on complex traits and disease. In this study, we apply the principles of Mendelian randomization to systematically evaluate transcriptome-wide associations between gene expression (across 48 different tissue types) and 395 complex traits. Our findings indicate that variants which influence gene expression levels in multiple tissues are more likely to influence multiple complex traits. Moreover, detailed investigations of our results highlight tissue-specific associations, drug validation opportunities, insight into the likely causal pathways for trait-associated variants and also implicate putative associations at loci yet to be implicated in disease susceptibility. Similar evaluations can be conducted at http://mrcieu.mrsoftware.org/Tissue_MR_atlas/.