Existing methods for graph out-of-distribution (OOD) detection typically depend on training graph neural network (GNN) classifiers using a substantial amount of labeled in-distribution (ID) data. However, acquiring high-quality labeled nodes in text-attributed graphs (TAGs) is challenging and costly due to their complex textual and structural characteristics. Large language models (LLMs), known for their powerful zero-shot capabilities in textual tasks, show promise but struggle to naturally capture the critical structural information inherent to TAGs, limiting their direct effectiveness. To address these challenges, we propose LLM-GOOD, a general framework that effectively combines the strengths of LLMs and GNNs to enhance data efficiency in graph OOD detection. Specifically, we first leverage LLMs' strong zero-shot capabilities to filter out likely OOD nodes, significantly reducing the human annotation burden. To minimize the usage and cost of the LLM, we employ it only to annotate a small subset of unlabeled nodes. We then train a lightweight GNN filter using these noisy labels, enabling efficient predictions of ID status for all other unlabeled nodes by leveraging both textual and structural information. After obtaining node embeddings from the GNN filter, we can apply informativeness-based methods to select the most valuable nodes for precise human annotation. Finally, we train the target ID classifier using these accurately annotated ID nodes. Extensive experiments on four real-world TAG datasets demonstrate that LLM-GOOD significantly reduces human annotation costs and outperforms state-of-the-art baselines in terms of both ID classification accuracy and OOD detection performance.