ST. LOUIS—Worries over immigrants potentially taking jobs from native-born Americans run high in parts of the nation, but some U.S. cities are taking a different view: Wooing immigrants can reverse long-term declines in population.

Cities, mostly in the Midwest and mid-Atlantic states, are betting that attracting foreign-born residents can spur business creation and revive neighborhoods. Steps vary from proclamations welcoming immigrants, to adding staff focused on attracting newcomers and translating government websites,...