Current AI agent architectures suffer from ephemeral memory limitations, preventing effective collaboration and knowledge sharing across sessions and agent boundaries. We introduce SAMEP (Secure Agent Memory Exchange Protocol), a novel framework that enables persistent, secure, and semantically searchable memory sharing among AI agents. Our protocol addresses three critical challenges: (1) persistent context preservation across agent sessions, (2) secure multi-agent collaboration with fine-grained access control, and (3) efficient semantic discovery of relevant historical context. SAMEP implements a distributed memory repository with vector-based semantic search, cryptographic access controls (AES-256-GCM), and standardized APIs compatible with existing agent communication protocols (MCP, A2A). We demonstrate SAMEP's effectiveness across diverse domains including multi-agent software development, healthcare AI with HIPAA compliance, and multi-modal processing pipelines. Experimental results show 73% reduction in redundant computations, 89% improvement in context relevance scores, and complete compliance with regulatory requirements including audit trail generation. SAMEP enables a new paradigm of persistent, collaborative AI agent ecosystems while maintaining security and privacy guarantees.