Collective cell migration underlies many biological processes, including embryonic development, wound healing, and cancer progression. In the embryo, cells have been observed to move collectively in vortices using a mode of collective migration known as coherent angular motion (CAM). To determine how CAM arises within a population and changes over time, here, we study the motion of mammary epithelial cells within engineered monolayers, in which the cells move collectively about a central axis in the tissue. Using quantitative image analysis, we find that CAM is significantly reduced when mitosis is suppressed. Particle-based simulations recreate the observed trends, suggesting that cell divisions drive the robust emergence of CAM and facilitate switches in the direction of collective rotation. Our simulations predict that the location of a dividing cell, rather than the orientation of the division axis, facilitates the onset of this motion. These predictions agree with experimental observations, thereby providing, to our knowledge, new insight into how cell divisions influence CAM within a tissue. Overall, these findings highlight the dynamic nature of CAM and suggest that regulating cell division is crucial for tuning emergent collective migratory behaviors, such as vortical motions observed in vivo.