The arrival of Generative Artificial Intelligence (GenAI) into higher education has brought about significant transformations in assessment practices and pedagogical approaches. Large Language Models (LLMs) powered by GenAI present unprecedented opportunities for personalised learning journeys. However, the emergence of GenAI in higher education raises concerns regarding academic integrity and the development of essential cognitive and creative skills among students. Critics worry about the potential decline in academic standards and the perpetuation of biases inherent in the training sets used for LLMs. Addressing these concerns requires clear frameworks and continual evaluation and updating of assessment practices to leverage GenAI's capabilities while preserving academic integrity. Here, we evaluated the integration of GenAI into a year-long MSc program to enhance student understanding and confidence in using GenAI. Approaching GenAI as a digital competency, its use was integrated into core skills modules across two semesters, focusing on ethical considerations, prompt engineering, and tool usage. The assessment tasks were redesigned to incorporate GenAI, which takes a process-based assessment approach. Students' perceptions were evaluated alongside skills audits, and they reported increased confidence in using GenAI. Thematic analysis of one-to-one interviews revealed a cyclical relationship between students' usage of GenAI, experience, ethical considerations, and learning adaptation.