Urban knowledge graph has recently worked as an emerging building block to distill critical knowledge from multi-sourced urban data for diverse urban application scenarios. Despite its promising benefits, urban knowledge graph construction (UrbanKGC) still heavily relies on manual effort, hindering its potential advancement. This paper presents UrbanKGent, a unified large language model agent framework, for urban knowledge graph construction. Specifically, we first construct the knowledgeable instruction set for UrbanKGC tasks (such as relational triplet extraction and knowledge graph completion) via heterogeneity-aware and geospatial-infused instruction generation. Moreover, we propose a tool-augmented iterative trajectory refinement module to enhance and refine the trajectories distilled from GPT-4. Through hybrid instruction fine-tuning with augmented trajectories on Llama 2 and Llama 3 family, we obtain UrbanKGC agents, consisting of UrbanKGent-7/8/13B version. We perform a comprehensive evaluation on two real-world datasets using both human and GPT-4 self-evaluation. The experimental results demonstrate that UrbanKGent family can not only significantly outperform 31 baselines in UrbanKGC tasks, but also surpass the state-of-the-art LLM, GPT-4, by more than 10% with approximately 20 times lower cost. Compared with the existing benchmark, the UrbanKGent family could help construct an UrbanKG with hundreds of times richer relationships using only one-fifth of the data. Our data and code are available at https://anonymous.4open.science/r/UrbanKGent_NeurIPS-B600.