To understand the biological mechanisms underlying thousands of genetic variants robustly associated with complex traits, scalable methods that integrate GWAS and functional data generated by large-scale efforts are needed. Here we propose a method termed MetaXcan that addresses this need by inferring the downstream consequences of genetically regulated components of molecular traits on complex phenotypes using summary data only. MetaXcan allows multiple causal variants and flexible multivariate models extending the capabilities of existing methods and enabling the testing of more complex processes. As an example application, we trained prediction models of gene expression levels in 44 human tissues and inferred the consequences of their regulation in 40 complex phenotypes. Our examination of this broad set of human tissues revealed many novel genes and re-identified known ones with patterns of regulation in expected as well as unexpected tissues.