Deep-learning-based gaze estimation approaches often suffer from notable performance degradation in unseen target domains. One of the primary reasons is that the Fully Connected layer is highly prone to overfitting when mapping the high-dimensional image feature to 3D gaze. In this paper, we propose Analytical Gaze Generalization framework (AGG) to improve the generalization ability of gaze estimation models without touching target domain data. The AGG consists of two modules, the Geodesic Projection Module (GPM) and the Sphere-Oriented Training (SOT). GPM is a generalizable replacement of FC layer, which projects high-dimensional image features to 3D space analytically to extract the principle components of gaze. Then, we propose Sphere-Oriented Training (SOT) to incorporate the GPM into the training process and further improve cross-domain performances. Experimental results demonstrate that the AGG effectively alleviate the overfitting problem and consistently improves the cross-domain gaze estimation accuracy in 12 cross-domain settings, without requiring any target domain data. The insight from the Analytical Gaze Generalization framework has the potential to benefit other regression tasks with physical meanings.