When users work with AI agents, they form conscious or subconscious expectations of them. Meeting user expectations is crucial for such agents to engage in successful interactions and teaming. However, users may form expectations of an agent that differ from the agent's planned behaviors. These differences lead to the consideration of two separate decision models in the planning process to generate explicable behaviors. However, little has been done to incorporate safety considerations, especially in a learning setting. We present Safe Explicable Policy Search (SEPS), which aims to provide a learning approach to explicable behavior generation while minimizing the safety risk, both during and after learning. We formulate SEPS as a constrained optimization problem where the agent aims to maximize an explicability score subject to constraints on safety and a suboptimality criterion based on the agent's model. SEPS innovatively combines the capabilities of Constrained Policy Optimization and Explicable Policy Search. We evaluate SEPS in safety-gym environments and with a physical robot experiment to show that it can learn explicable behaviors that adhere to the agent's safety requirements and are efficient. Results show that SEPS can generate safe and explicable behaviors while ensuring a desired level of performance w.r.t. the agent's objective, and has real-world relevance in human-AI teaming.