Spatio-temporal graph neural networks have demonstrated efficacy in capturing complex dependencies for urban computing tasks such as forecasting and kriging. However, their performance is constrained by the reliance on extensive data for training on specific tasks, which limits their adaptability to new urban domains with varied demands. Although transfer learning has been proposed to address this problem by leveraging knowledge across domains, cross-task generalization remains underexplored in spatio-temporal graph transfer learning methods due to the absence of a unified framework. To bridge this gap, we propose Spatio-Temporal Graph Prompting (STGP), a prompt-enhanced transfer learning framework capable of adapting to diverse tasks in data-scarce domains. Specifically, we first unify different tasks into a single template and introduce a task-agnostic network architecture that aligns with this template. This approach enables the capture of spatio-temporal dependencies shared across tasks. Furthermore, we employ learnable prompts to achieve domain and task transfer in a two-stage prompting pipeline, enabling the prompts to effectively capture domain knowledge and task-specific properties at each stage. Extensive experiments demonstrate that STGP outperforms state-of-the-art baselines in three downstream tasks forecasting, kriging, and extrapolation by a notable margin.