Robotic object packing has broad practical applications in the logistics and automation industry, often formulated by researchers as the online 3D Bin Packing Problem (3D-BPP). However, existing DRL-based methods primarily focus on enhancing performance in limited packing environments while neglecting the ability to generalize across multiple environments characterized by different bin dimensions. To this end, we propose GOPT, a generalizable online 3D Bin Packing approach via Transformer-based deep reinforcement learning (DRL). First, we design a Placement Generator module to yield finite subspaces as placement candidates and the representation of the bin. Second, we propose a Packing Transformer, which fuses the features of the items and bin, to identify the spatial correlation between the item to be packed and available sub-spaces within the bin. Coupling these two components enables GOPT's ability to perform inference on bins of varying dimensions. We conduct extensive experiments and demonstrate that GOPT not only achieves superior performance against the baselines, but also exhibits excellent generalization capabilities. Furthermore, the deployment with a robot showcases the practical applicability of our method in the real world. The source code will be publicly available at https://github.com/Xiong5Heng/GOPT.