Background: In view of the widespread use of digital technologies in English as a foreign language (EFL) learning and the importance of students' approaches to learning (SAL) and digital competence, as well as the threats of technostress in digital settings, digital EFL learning requires a critical examination. Objectives: This study sought to investigate the interrelationships among of SAL, students' digital competence, and the emerging technostress in digital learning of EFL. Methods: Survey and EFL test data of 477 university students taking EFL courses were collected. Partial least square structural equation modelling and cluster analysis were employed to analyze these data. Results and Conclusions: The results indicate that a surface approach to learning was significantly positively associated with technostress while negatively associated with digital competence. The deep and organized learning approaches positively predicted digital competence, which further negatively predicted technostress and burnout in digital learning of EFL. Technostress was found to be positively related to exhaustion and cynicism, with cynicism being negatively related to EFL learning outcomes. The cluster analysis identified three clusters of EFL learners and revealed that, overall, high scores in the deep and organized approaches to learning were generally aligned with strong digital competence, low technostress, low burnout, and high EFL learning outcomes. Takeaways: The findings of this study carry important implications for practitioners of EFL learning and teaching in the design of strategies, pedagogies, and EFL learning technologies that improve EFL learning in digital settings while maintaining learners' wellbeing.