This article introduces Follow-Me AI, a concept designed to enhance user interactions with smart environments, optimize energy use, and provide better control over data captured by these environments. Through AI agents that accompany users, Follow-Me AI negotiates data management based on user consent, aligns environmental controls as well as user communication and computes resources available in the environment with user preferences, and predicts user behavior to proactively adjust the smart environment. The manuscript illustrates this concept with a detailed example of Follow-Me AI in a smart campus setting, detailing the interactions with the building's management system for optimal comfort and efficiency. Finally, this article looks into the challenges and opportunities related to Follow-Me AI.