Long-term music training can positively impact speech processing. A recent framework developed to explain such cross-domain plasticity posits that music training-related advantages in speech processing are due to shared cognitive and perceptual processes between music and speech. Although perceptual and cognitive processing advantages due to music training have been independently demonstrated, to date no study has examined perceptual and cognitive processing within the context of a single task. The present study examines the impact of long-term music training on speech learning from a rigorous, computational perspective derived from signal detection theory. Our computational models provide independent estimates of cognitive and perceptual processing in native English-speaking musicians (n = 15, mean age = 25 years) and non-musicians (n = 15, mean age = 23 years) learning to categorize non-native lexical pitch patterns (Mandarin tones). Musicians outperformed non-musicians in this task. Model-based analyses suggested that musicians shifted from simple unidimensional decision strategies to more optimal multidimensional (MD) decision strategies sooner than non-musicians. In addition, musicians used optimal decisional strategies more often than non-musicians. However, musicians and non-musicians who used MD strategies showed no difference in performance. We estimated parameters that quantify the magnitude of perceptual variability along two dimensions that are critical for tone categorization: pitch height and pitch direction. Both musicians and non-musicians showed a decrease in perceptual variability along the pitch height dimension, but only musicians showed a significant reduction in perceptual variability along the pitch direction dimension. Notably, these advantages persisted during a generalization phase, when no feedback was provided. These results provide an insight into the mechanisms underlying the musician advantage observed in non-native speech learning.