Anomaly detection on text-rich graphs is widely prevalent in real life, such as detecting incorrectly assigned academic papers to authors and detecting bots in social networks. The remarkable capabilities of large language models (LLMs) pave a new revenue by utilizing rich-text information for effective anomaly detection. However, simply introducing rich texts into LLMs can obscure essential detection cues and introduce high fine-tuning costs. Moreover, LLMs often overlook the intrinsic structural bias of graphs which is vital for distinguishing normal from abnormal node patterns. To this end, this paper introduces GuARD, a text-rich and graph-informed language model that combines key structural features from graph-based methods with fine-grained semantic attributes extracted via small language models for effective anomaly detection on text-rich graphs. GuARD is optimized with the progressive multi-modal multi-turn instruction tuning framework in the task-guided instruction tuning regime tailed to incorporate both rich-text and structural modalities. Extensive experiments on four datasets reveal that GuARD outperforms graph-based and LLM-based anomaly detection methods, while offering up to 5$\times$ times speedup in training and 5$\times$ times speedup in inference over vanilla long-context LLMs on the large-scale WhoIsWho dataset.