While Generative Artificial Intelligence (GenAI) technologies like ChatGPT are revolutionizing education by offering unique interaction opportunities and prompting legislative shifts toward AI literacy, there remains a significant gap in understanding the factors that influence their acceptance and effective use in educational settings. In particular, the impact of students' digital competencies and motivational factors on their acceptance and utilization of GenAI tools is not well understood. This study investigates how these variables influence undergraduate students' acceptance and use of ChatGPT as an informal learning tool, aiming to advance understanding of GenAI adoption in higher education. By integrating the Digital Competence Framework (DigComp) with the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2), this research provides a comprehensive analysis of factors affecting students' intention to use and actual use of ChatGPT. Data were collected from 544 undergraduate students using adapted UTAUT2 scales and digital competence measures aligned with DigComp. Confirmatory Factor Analysis (n = 140) validated the adapted UTAUT2, and Structural Equation Modeling (n = 404) explored relationships between variables. The findings reveal that habit, hedonic motivation, performance expectancy, and facilitating conditions significantly predict students' intention to use ChatGPT, while behavioral intention, problem-solving skills, and ethical considerations positively influence actual use. Notably, the study highlights the critical role of problem-solving and ethical awareness--in the adoption of GenAI tools. These results suggest that existing digital competence frameworks may need updating to include GenAI-specific competencies such as prompt-writing skills, managing ongoing dialogs with GenAI tools, and critically evaluating AI-generated content.