Large language models (LLMs) have shown strong performance in static code tasks like code search, summarization, and generation, but remain limited in dynamic code reasoning, which involves inferring how programs behave during execution without actually running them. This limitation stems from LLMs being trained on static code and lacking the necessary runtime context. In this paper, we present T-REX, a novel teacher-student framework for execution prediction that addresses these limitations by grounding LLM training in actual execution and corresponding execution semantics. T-REX uses a large teacher model (Explainer) to generate fine-grained, stepwise natural language rationales explaining how program state transitions from one statement to another during actual execution. These rationales are used to train a smaller student model (Reasoner) to predict next program states, enabling accurate simulation of program behavior with lower computational cost. Our execution-grounded, rationale-driven training aligns with transition-aware execution semantics at the statement level, enhancing prediction accuracy. Our experiments show that T-REX enables Reasoner to outperform much larger GPT-4o and GPT-4o-mini models across multiple dimensions of runtime behavior prediction, while also aiding in static detection of runtime errors as well as in debugging. Finally, we discuss how T-REX can be generalized to static emulation of any dynamic analysis through such a teacher-student distillation, illustrating with the specific case of dynamic program slicing in Python.