(1) Background: Globally, the kidney donor shortage has made the allocation process critical for patients awaiting a kidney transplant. Adopting Machine Learning (ML) models for donor-recipient matching can potentially improve kidney allocation processes when compared with traditional points-based systems. (2) Methods: This study developed an ML-based approach for donor-recipient matching. A comprehensive evaluation was conducted using ten widely used classifiers (logistic regression, decision tree, random forest, support vector machine, gradient boosting, boost, CatBoost, LightGBM, naive Bayes, and neural networks) across three experimental scenarios to ensure a robust approach. The first scenario used the original dataset, the second used a merged version of the dataset, and the last scenario used a hierarchical architecture model. Additionally, a custom ranking algorithm was designed to identify the most suitable recipients. Finally, the ML-based donor-recipient matching model was integrated into a web-based platform called Nephron. (3) Results: The gradient boost model was the top performer, achieving a remarkable and consistent accuracy rate of 98% across the three experimental scenarios. Furthermore, the custom ranking algorithm outperformed the conventional cosine and Jaccard similarity methods in identifying the most suitable recipients. Importantly, the platform not only facilitated efficient patient selection and prioritisation for kidney allocation but can be flexibly adapted for other solid organ allocation systems built on similar criteria. (4) Conclusions: This study proposes an ML-based approach to optimize donor-recipient matching within the kidney allocation process. Successful implementation of this methodology demonstrates significant potential to enhance both efficiency and fairness in kidney transplantation.