The adoption of Sustainable Healthy Diets (SHDs) plays a crucial role in both environmental sustainability and nutritional adequacy, preventing malnutrition, obesity, and natural resource degradation. Despite extensive research on sustainability, nutrition, and human behaviors related to food consumption, gaps remain in understanding how to effectively promote the adoption of SHDs, especially among vulnerable populations. This systematic literature review (SLR) identifies and analyzes drivers and barriers that influence the adoption of SHDs in high- and upper-middle-income countries, offering insights for policymakers and stakeholders to develop informed actions. A total of 156 studies were analyzed to extract insights into the ecological, economic, human health, and sociocultural dimensions, revealing 19 key driver themes, such as environmental and nutritional education and awareness, financial incentives, and community engagement. Conversely, 22 barriers were identified, including the high costs of adopting SHDs, social and cultural resistance to dietary changes, and limited access to nutritious options, especially in low-income areas. The proposed “SHDs Barriers & Drivers” framework offers an intuitive representation of these multifaceted factors, highlighting the central role of human behavior. Limitations include the potential exclusion of relevant studies due to specific keyword selection and the focus on high- and upper-middle-income countries. The research contributes to the existing literature by offering an innovative view of how to leverage the importance of tailored and multidisciplinary approaches to foster sustainable nutrition and achieve both global health and sustainability goals.