Here, we present a joint-tissue imputation (JTI) approach and a Mendelian randomization framework for causal inference, MR-JTI. JTI borrows information across transcriptomes of different tissues, leveraging shared genetic regulation, to improve prediction performance in a tissue-dependent manner. Notably, JTI includes the single-tissue imputation method PrediXcan as a special case and outperforms other single-tissue approaches (the Bayesian sparse linear mixed model and Dirichlet process regression). MR-JTI models variant-level heterogeneity (primarily due to horizontal pleiotropy, addressing a major challenge of transcriptome-wide association study interpretation) and performs causal inference with type I error control. We make explicit the connection between the genetic architecture of gene expression and of complex traits and the suitability of Mendelian randomization as a causal inference strategy for transcriptome-wide association studies. We provide a resource of imputation models generated from GTEx and PsychENCODE panels. Analysis of biobanks and meta-analysis data, and extensive simulations show substantially improved statistical power, replication and causal mapping rate for JTI relative to existing approaches.