President Donald Trump chose an active-duty Army general as his new national security adviser on Monday, bringing one of the U.S. military’s best-known strategists into the White House and adding to his team another warrior-scholar in the mold of Defense Secretary Jim Mattis.

Lt. Gen. H.R. McMaster, whom Mr. Trump called “a man of tremendous talent and tremendous experience,” accepted the post, making him the first active-duty U.S. military officer to take the job since Colin Powell and John Poindexter held it under President...