Graph Neural Networks (GNNs) have gained great popularity in tackling various analytical tasks on graph-structured data (i.e., networks). Typical GNNs and their variants follow a message-passing manner that obtains network representations by the feature propagation process along network topology, which however ignore the rich textual semantics (e.g., local word-sequence) that exist in many real-world networks. Existing methods for text-rich networks integrate textual semantics by mainly utilizing internal information such as topics or phrases/words, which often suffer from an inability to comprehensively mine the text semantics, limiting the reciprocal guidance between network structure and text semantics. To address these problems, we propose a novel text-rich graph neural network with external knowledge (TeKo), in order to take full advantage of both structural and textual information within text-rich networks. Specifically, we first present a flexible heterogeneous semantic network that incorporates high-quality entities and interactions among documents and entities. We then introduce two types of external knowledge, that is, structured triplets and unstructured entity description, to gain a deeper insight into textual semantics. We further design a reciprocal convolutional mechanism for the constructed heterogeneous semantic network, enabling network structure and textual semantics to collaboratively enhance each other and learn high-level network representations. Extensive experimental results on four public text-rich networks as well as a large-scale e-commerce searching dataset illustrate the superior performance of TeKo over state-of-the-art baselines.