Artificial intelligence (AI) is reshaping how financial institutions identify, evaluate, price, and allocate capital toward environmentally oriented activities. Yet scholarship on AI-enabled green-finance decision-making remains fragmented across finance, accounting, information systems, computer science, and sustainability research, and no prior review has organized this evidence around the decision tasks that financial actors actually perform. This systematic literature review (SLR), conducted in accordance with the PRISMA 2020 guidelines, synthesizes 107 peer-reviewed journal articles published between January 2010 and May 2026, retrieved from Scopus and Web of Science using a pre-specified three-block search strategy and screened by two independent reviewers (Cohen's kappa = 0.81). We develop an integrative framework that links AI capabilities, green-finance decision tasks, governance filters, and outcome criteria, and we organize the corpus around six decision-task clusters: ESG scoring and sustainability assessment, green credit and lending decisions, climate-aware portfolio construction, sustainability-disclosure analysis, green-bond and carbon-market applications, and algorithmic governance and Green AI. Three cross-cutting tensions structure the field: the trade-off between predictive accuracy and interpretability, the problem of contested and inconsistent sustainability data, and the environmental footprint of AI itself. Our central contribution is a re-framing of the debate from whether AI improves prediction to when AI improves green-finance decisions under conditions of data uncertainty, model opacity, and sustainability accountability. We translate the synthesis into a six-item research agenda covering decision-level validation, causal identification, explainable and energy-aware modelling, greenwashing detection, cross-jurisdictional comparability, and Green-AI governance