WASHINGTON—President Barack Obama plans to dramatically boost the U.S. effort to mitigate the Ebola outbreak in West Africa, including greater involvement of the U.S. military, people familiar with the proposal said. (Ebola virus latest: First U.S. case confirmed).

Mr. Obama is expected to detail the plan during a visit Tuesday to the Centers for Disease Control and Prevention in Atlanta, these people said. Among the possible moves: sending additional portable hospitals, doctors and health-care experts, providing medical supplies...