President-elect Donald Trump has selected Elaine Chao to be his transportation secretary on Tuesday.

Ms. Chao, who is married to Senate Majority Leader Mitch McConnell of Kentucky, would join South Carolina Gov. Nikki Haley, tapped for U.S. ambassador to the United Nations, and charter-school advocate Betsy DeVos, picked for education secretary, as women named to top roles in the Trump administration.

If...