This paper proposes the Transition Motion Tensor, a data-driven framework that creates novel and physically accurate transitions outside of the motion dataset. It enables simulated characters to adopt new motion skills efficiently and robustly without modifying existing ones. Given several physically simulated controllers specializing in different motions, the tensor serves as a temporal guideline to transition between them. Through querying the tensor for transitions that best fit user-defined preferences, we can create a unified controller capable of producing novel transitions and solving complex tasks that may require multiple motions to work coherently. We apply our framework on both quadrupeds and bipeds, perform quantitative and qualitative evaluations on transition quality, and demonstrate its capability of tackling complex motion planning problems while following user control directives.