Study success includes the successful completion of a first degree in higher education to the largest extent, and the successful completion of individual learning tasks to the smallest extent. Factors affecting study success range from individual dispositions (e.g., motivation, prior academic performance) to characteristics of the educational environment (e.g., attendance, active learning, social embeddedness). Recent developments in learning analytics, which are a socio-technical data mining and analytic practice in educational contexts, show promise in enhancing study success in higher education, through the collection and analysis of data from learners, learning processes, and learning environments in order to provide meaningful feedback and scaffolds when needed. This research reports a systematic review focusing on empirical evidence, demonstrating how learning analytics have been successful in facilitating study success in continuation and completion of students' university courses. Using standardised steps of conducting a systematic review, an initial set of 6220 articles was identified. The final sample includes 46 key publications. The findings obtained in this systematic review suggest that there are a considerable number of learning analytics approaches which utilise effective techniques in supporting study success and students at risk of dropping out. However, rigorous, large-scale evidence of the effectiveness of learning analytics in supporting study success is still lacking. The tested variables, algorithms, and methods collected in this systematic review can be used as a guide in helping researchers and educators to further improve the design and implementation of learning analytics systems.