The last years have seen an acceleration in the development and uptake of artificial intelligence (AI) systems by "early adopter" hospitals, caught between the pressures to "perform" and "transform" in a struggling health care system. This transformation has raised concerns among health care providers as their voices and location-specific workflows have often been overlooked, resulting in technologies that fail to integrate meaningfully into routine care and worsen rather than improve care processes. How can positive AI implementation be carried out in health care, aligned with European values? Based on a perspective that spans all stakeholders, we have created EURAID (European Responsible AI Development), a practical, human-centric framework for AI development and implementation based on agreed goals and values. We illustrate this approach through the co-development of a narrow-purpose "in-house" AI system, designed to help bridge the AI implementation gap in real-world clinical settings. This example is then expanded to address the broader challenges associated with complex, multiagent AI systems. By portraying all key stakeholders across the AI development life cycle and highlighting their roles and contributions within the process, real use cases, and methods for achieving iterative consensus, we offer a unique practical approach for safe and fast progress in hospital digital transformation in the AI age.