ChatGPT, a state-of-the-art artificial intelligence (AI) chatbot, has gained considerable attention as a transformative yet controversial tool for enhancing teaching and learning experiences. Several reviews and numerous articles have been written about harnessing ChatGPT in education since its release on November 30, 2022. Besides summarising its strengths, weaknesses, opportunities, and threats (SWOT) as identified in previous systematic reviews of ChatGPT research, this systematic review aims to develop a new understanding of its influence on student engagement by synthesising the existing related research using a three-dimensional framework comprising behavioural, emotional, and cognitive aspects. We searched relevant databases and included 72 empirical studies published within one year of ChatGPT's initial release. The findings reveal robust but narrowly focused evidence related to behavioural engagement (i.e., work with ChatGPT) and disengagement (i.e., academic dishonesty). The evidence related to the emotional aspect is mixed, with instances of both engagement (e.g., satisfaction and interest/fun) and disengagement (e.g., disappointment and worry/anxiety). There is broad but weak evidence regarding cognitive engagement (e.g., increased understanding and positive self-perception) and disengagement (e.g., reduced critical thinking and overreliance). Our review uncovers several under-explored indicators of student engagement, pointing to the need for further research. Specifically, future studies could focus on students' study habits and attendance (behavioural engagement), social interaction (emotional engagement), and self-regulation and critical thinking (cognitive engagement) in ChatGPT-supported learning environments.