Sequence-to-Sequence (Seq2Seq) neural text generation models, especially the pre-trained ones (e.g., BART and T5), have exhibited compelling performance on various natural language generation tasks. However, the black-box nature of these models limits their application in tasks where specific rules (e.g., controllable constraints, prior knowledge) need to be executed. Previous works either design specific model structures (e.g., Copy Mechanism corresponding to the rule "the generated output should include certain words in the source input'') or implement specialized inference algorithms (e.g., Constrained Beam Search) to execute particular rules through the text generation. These methods require the careful design case-by-case and are difficult to support multiple rules concurrently. In this paper, we propose a novel module named Neural Rule-Execution Tracking Machine (NRETM) that can be equipped into various transformer-based generators to leverage multiple rules simultaneously to guide the neural generation model for superior generation performance in an unified and scalable way. Extensive experiments on several benchmarks verify the effectiveness of our proposed model in both controllable and general text generation tasks.