As a marriage between offline RL and meta-RL, the advent of offline meta-reinforcement learning (OMRL) has shown great promise in enabling RL agents to multi-task and quickly adapt while acquiring knowledge safely. Among which, context-based OMRL (COMRL) as a popular paradigm, aims to learn a universal policy conditioned on effective task representations. In this work, by examining several key milestones in the field of COMRL, we propose to integrate these seemingly independent methodologies into a unified framework. Most importantly, we show that the pre-existing COMRL algorithms are essentially optimizing the same mutual information objective between the task variable $M$ and its latent representation $Z$ by implementing various approximate bounds. Such theoretical insight offers ample design freedom for novel algorithms. As demonstrations, we propose a supervised and a self-supervised implementation of $I(Z; M)$, and empirically show that the corresponding optimization algorithms exhibit remarkable generalization across a broad spectrum of RL benchmarks, context shift scenarios, data qualities and deep learning architectures. This work lays the information theoretic foundation for COMRL methods, leading to a better understanding of task representation learning in the context of reinforcement learning. Given its generality, we envision our framework as a promising offline pre-training paradigm of foundation models for decision making.