Generative artificial intelligence (GenAI) is increasingly integrated into higher education, where it supports writing, feedback, problem solving, and research-related tasks while also raising concerns about cognitive offloading and learner dependence. This scoping review maps the literature on the relationships among GenAI, cognitive offloading, and learner agency in higher education. Following PRISMA-ScR guidance, searches were conducted on 24 June 2026 across six database sources: Web of Science Core Collection, Scopus, EBSCOhost ERIC, EBSCOhost Education Source, APA PsycInfo via ProQuest, and ProQuest Education Collection via ProQuest Social Science Premium Collection. English-language peer-reviewed or scholarly journal literature published from 2022 to 24 June 2026 was eligible for inclusion. Data were charted using a structured extraction matrix and synthesized through descriptive mapping and theory-informed configurative synthesis. After duplicate removal, 5327 records were screened by title and abstract, 691 full-text reports were assessed, and 123 studies were included in the final charting matrix and synthesis. The review shows that learner agency is conceptualized as a multidimensional construct involving self-regulation, reflective judgement, intentionality, and responsible action. Across the literature, GenAI is best interpreted through an interpretive dual-pattern account: agency-supportive patterns are associated with self-regulated learning, self-efficacy, feedback literacy, and reflective engagement, whereas agency-eroding patterns are associated with cognitive offloading, overreliance, dependence, uncritical uptake, and weakened judgement. These patterns should be interpreted as a configurative synthesis of heterogeneous evidence rather than as causal effect estimates. Overall, the findings suggest that the educational value of GenAI depends less on the technology itself than on how it is pedagogically embedded, with augmentation-oriented and scaffolded use being more supportive of learner agency than replacement-oriented use.