More recently, there has been a surge of interest in employing machine learning approaches to expedite the drug discovery process where virtual screening for hit discovery and ADMET prediction for lead optimization play essential roles. One of the main obstacles to the wide success of machine learning approaches in these two tasks is that the number of compounds labeled with activities or ADMET properties is too small to build an effective predictive model. This paper seeks to remedy the problem by transferring the knowledge from previous assays, namely in-vivo experiments, by different laboratories and against various target proteins. To accommodate these wildly different assays and capture the similarity between assays, we propose a functional rationalized meta-learning algorithm FRML for such knowledge transfer. FRML constructs the predictive model with layers of neural sub-networks or so-called functional regions. Building on this, FRML shares an initialization for the weights of the predictive model across all assays, while customizes it to each assay with a region localization network choosing the pertinent regions. The compositionality of the model improves the capacity of generalization to various and even out-of-distribution tasks. Empirical results on both virtual screening and ADMET prediction validate the superiority of FRML over state-of-the-art baselines powered with interpretability in assay relationship.