The ability to predict diseases is critical in healthcare for early intervention and better patient outcomes. Data security and privacy significantly classified medical data from several institutions is analyzed. Cooperative model training provided by Federated Learning (FL), preserves data privacy. In this study, we offer a fusion strategy for illness prediction, combining FL with Anova and Chi-Square Feature Selection (FS) and Linear Discriminate Analysis (LDA) Feature Extraction (FE) techniques. This research aims to use FS and FE techniques to improve prediction performance while using the beneficial aspects of FL. A comprehensive analysis of the distributed data is ensured by updating aggregate models with information from all participating institutions. Through collaboration, a robust disease prediction system excels in the limited possibilities of individual datasets. We assessed the fusion strategy on the Cleveland heart disease and diabetes datasets from the UCI repository. Comparing the fusion strategy to solo FL or conventional ML techniques, the prediction performance a unique fusion methodology for disease prediction. Our proposed models, Chi-Square with LDA and Anova with LDA leveraging FL, exhibited exceptional performance on the diabetes dataset, achieving identical accuracy, precision, recall, and f1-score of 92.3%, 94.36%, 94.36, and 94.36%, respectively. Similarly, on the Cleveland heart disease dataset, these models demonstrated significant performance, achieving accuracy, precision, recall, and f1-score of 88.52%, 87.87%, 90.62, and 89.23%, respectively. The results have the potential to revolutionize disease prediction, maintain privacy, advance healthcare, and outperform state-of-the-art models.