Artificial intelligence is fundamentally transforming synthetic biology biosensors (SBBs) from traditional rational design to AI-driven predictive engineering. This review establishes the first systematic integration framework of AI algorithms with the design-build-test-learn (DBTL) full cycle of synthetic biology biosensors, clearly dissecting the differentiated engineering paradigms of AI-enabled cellular SBBs and AI-optimized cell-free SBBs. It reveals the core mechanisms of computational intelligence in overcoming specific technical bottlenecks for these two sensing platforms. The study summarizes the AI-driven SBB engineering process into three core frontier directions: AI-guided robust sensing element design, AI-assisted signal processing and performance characterization, and AI-driven closed-loop optimization and autonomous evolution. Meanwhile, it systematically reviews the representative application advancements of AI-enabled SBBs in four major fields: environmental monitoring, continuous clinical biomarker detection, food safety traceability, and intelligent biofabrication. Finally, this research critically evaluates unresolved core challenges such as the "reality gap" and "small data dilemma" in the field, proposing a technical roadmap centered on bio-digital hybrid interfaces, explainable AI, and standardized data systems. It provides comprehensive theoretical guidance and practical directions for advancing synthetic biology biosensors from laboratory prototypes to robust, field-deployable next-generation intelligent sensing systems.