Two Texas hospital giants announced they plan to merge, which would combine dominant hospital systems in two of the nation’s largest metropolitan markets, one of the latest signs of the consolidation reshaping the health-care industry.

Baylor Scott & White Health, a nonprofit based in Dallas, and Memorial Hermann Health System, based in Houston and also a nonprofit, announced a letter of intent to create a 68-hospital system spanning from the Gulf of Mexico to the Oklahoma border.

The...