The U.S. military will deploy about 3,000 personnel to West Africa to coordinate international aid, build treatment centers and train health-care workers as part of President Barack Obama’s offensive against a rapidly worsening Ebola outbreak, a senior administration official said Monday. (Latest:U.S. soldiers race to build Ebola treatment centers in Liberia).

The military will make up the largest component of an intensified U.S. government response to the outbreak that Mr. Obama plans to discuss during a visit to the Centers...