We propose a novel 3D gaze redirection framework that leverages an explicit 3D eyeball structure. Existing gaze redirection methods are typically based on neural radiance fields, which employ implicit neural representations via volume rendering. Unlike these NeRF-based approaches, where the rotation and translation of 3D representations are not explicitly modeled, we introduce a dedicated 3D eyeball structure to represent the eyeballs with 3D Gaussian Splatting (3DGS). Our method generates photorealistic images that faithfully reproduce the desired gaze direction by explicitly rotating and translating the 3D eyeball structure. In addition, we propose an adaptive deformation module that enables the replication of subtle muscle movements around the eyes. Through experiments conducted on the ETH-XGaze dataset, we demonstrate that our framework is capable of generating diverse novel gaze images, achieving superior image quality and gaze estimation accuracy compared to previous state-of-the-art methods.