The integration of renewable energy sources into power grids is a critical challenge for developing economies, where infrastructure limitations, unpredictable energy demand, and policy gaps hinder effective energy transitions. Machine learning (ML) offers transformative potential in addressing these challenges, enabling more efficient and reliable energy systems through advanced data analytics, predictive modeling, and real-time decision-making. This review explores how ML can optimize renewable energy integration by improving forecasting accuracy, enhancing grid stability, and optimizing resource allocation in solar, wind, and hydropower systems. Machine learning algorithms are particularly effective in predicting energy demand and renewable resource availability, allowing for better alignment between energy supply and consumption patterns. By leveraging ML-based predictive models, grid operators can mitigate the risks of energy shortages or oversupply, improve grid stability, and reduce operational costs. Furthermore, the application of ML in renewable energy systems provides opportunities for developing economies to leapfrog traditional energy infrastructure limitations by adopting smart grids that integrate real-time data to enhance decision-making and efficiency. This review also reviews case studies from Africa and Latin America, highlighting successful implementations of ML in renewable energy systems. These examples underscore the potential for ML to accelerate the deployment of sustainable energy solutions, while also addressing technical, economic, and policy barriers that exist in developing contexts. With continued advancements in machine learning, combined with supportive regulatory frameworks and investment in digital infrastructure, developing economies have the potential to realize substantial gains in renewable energy integration. This review concludes by discussing future trends, challenges, and opportunities for leveraging machine learning to optimize renewable energy integration, ultimately contributing to sustainable development and energy security in emerging markets.