Collective migration -- the directed, coordinated motion of many self-propelled agents -- is a fascinating emergent behavior exhibited by active matter that has key functional implications for biological systems. Extensive studies have elucidated the different ways in which this phenomenon may arise. Nevertheless, how collective migration can persist when a population is confronted with perturbations, which inevitably arise in complex settings, is poorly understood. Here, by combining experiments and simulations, we describe a mechanism by which collectively migrating populations smooth out large-scale perturbations in their overall morphology, enabling their constituents to continue to migrate together. We focus on the canonical example of chemotactic migration of Escherichia coli, in which fronts of cells move via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We identify two distinct modes in which chemotaxis influences the morphology of the population: cells in different locations along a front migrate at different velocities due to spatial variations in (i) the local nutrient gradient and in (ii) the ability of cells to sense and respond to the local nutrient gradient. While the first mode is destabilizing, the second mode is stabilizing and dominates, ultimately driving smoothing of the overall population and enabling continued collective migration. This process is autonomous, arising without any external intervention; instead, it is a population-scale consequence of the manner in which individual cells transduce external signals. Our findings thus provide insights to predict, and potentially control, the collective migration and morphology of cell populations and diverse other forms of active matter.