Functional MRI (fMRI) is crucial for studying brain function and diagnosing neurological disorders. However, existing analysis methods suffer from reproducibility and transferability challenges due to complex preprocessing pipelines and task-specific model designs. In this work, we introduce NeuroSTORM (Neuroimaging Foundation Model with Spatial-Temporal Optimized Representation Modeling) that learns generalizable representations directly from 4D fMRI volumes and enables efficient transfer to diverse downstream applications. Specifically, NeuroSTORM is pre-trained on 28.65 million fMRI frames from over 50,000 subjects, spanning multiple centers and ages 5 to 100. It combines an efficient spatiotemporal modeling design and lightweight task adaptation to enable scalable pre-training and fast transfer to downstream applications. Here we show that NeuroSTORM consistently outperforms existing methods across five downstream tasks, including demographic prediction, phenotype prediction, disease diagnosis, re-identification, and state classification. On two multi-hospital clinical cohorts with 17 diagnoses, NeuroSTORM achieves the best diagnosis performance while remaining predictive of psychological and cognitive phenotypes. These results suggest that NeuroSTORM could become a standardized foundation model for reproducible and transferable fMRI analysis.