Trace eyelid conditioning is a form of associative learning that requires several forebrain structures and cerebellum. Previous work suggests that at least two conditioned stimulus (CS)-driven signals are available to the cerebellum via mossy fiber inputs during trace conditioning: one driven by and terminating with the tone and a second driven by medial prefrontal cortex (mPFC) that persists through the stimulus-free trace interval to overlap in time with the unconditioned stimulus (US). We used electric stimulation of mossy fibers to determine whether this pattern of dual inputs is necessary and sufficient for cerebellar learning to express normal trace eyelid responses. We find that presenting the cerebellum with one input that mimics persistent activity observed in mPFC and the lateral pontine nuclei during trace eyelid conditioning and another that mimics tone-elicited mossy fiber activity is sufficient to produce responses whose properties quantitatively match trace eyelid responses using a tone. Probe trials with each input delivered separately provide evidence that the cerebellum learns to respond to the mPFC-like input (that overlaps with the US) and learns to suppress responding to the tone-like input (that does not). This contributes to precisely timed responses and the well-documented influence of tone offset on the timing of trace responses. Computer simulations suggest that the underlying cerebellar mechanisms involve activation of different subsets of granule cells during the tone and during the stimulus-free trace interval. These results indicate that tone-driven and mPFC-like inputs are necessary and sufficient for the cerebellum to learn well-timed trace conditioned responses.