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Developing effective machine learning models requires complex manual tuning, while current Automated Machine Learning (AutoML) frameworks remain domain-specific and isolate model architecture, training hyperparameter, and data ratio optimization. Here, we bridge this gap by proposing a universal, large language model (LLM)-based AutoML framework that jointly optimizes these configurations for the first time without the need for task-specific fine-tuning. We propose NCode, a unified numerical encoding scheme that translates diverse AutoML design choices into universal discrete sequences and effectively reframes the optimization process as a unified ranking task. Trained solely on optimization trajectories derived from a limited, single-domain vision task, the proposed LLM-based searcher demonstrates impressive cross-task, cross-modality and joint search-space optimization generalizability, achieving state-of-the-art performance across image classification, image segmentation, speaker verification and text-to-image benchmarks. Crucially, it exhibits superior scalability in the large-scale training and joint optimization of a billion-parameter Diffusion Transformer, requiring 896 GPU-days and attaining a state-of-the-art GenEval score of 0.91. By leveraging reinforcement learning to instill Chain-of-Thought reasoning, we provide a systematic way to interpret the LLM-based searcher's internal decision-making mechanisms, revealing its optimization strategy shifted from the early-stage diversity-driven exploration to the late-stage anchor exploitation. Our proposed framework provides a scalable, generalizable, and interpretable pathway toward general-purpose open-world machine learning optimization.