This study aimed to examine the reciprocal relationship between motivation and engagement in out-of-class learning among Japanese undergraduates by using a cross-lagged panel model. Two online surveys were conducted with 293 university students in Japan. This study measured motivation and engagement with regard to out-of-class tasks (homework) for compulsory classes relating to the university students' major subjects. Hypothesis 1 posited that there would be a positive reciprocal relationship between intrinsic/identified regulation and engagement in out-of-class learning. Hypothesis 2 posited that there would be a negative or no reciprocal relationships between introjected/external regulation and engagement in out-of-class learning. The results of the cross-lagged panel model partially supported each hypothesis. A positive reciprocal relationship between intrinsic regulation and emotional engagement was found. In addition, identified and introjected regulation in the first survey were positively correlated with behavioral engagement in the second survey. However, no relationship was observed between external regulation and engagement. Thus, intrinsic, identified, and introjected regulation were revealed as important factors in promoting engagement in out-of-class learning. Based on this study's findings, practical implications for education regarding motivation and engagement in out-of-class learning were proposed.