President-elect Donald J. Trump chose Pete Hegseth, a Fox News host and veteran of the wars in Iraq and Afghanistan, to be his next defense secretary, elevating a television ally to run the Pentagon and lead 1.3 million active-duty troops.

The choice of Mr. Hegseth was outside the norm of the traditional defense secretary, but he was a dedicated supporter of Mr. Trump during his first term, defending his interactions with the North Korean leader Kim Jong-un, embracing his “America First” agenda of trying to withdraw U.S. troops from abroad and energetically taking up the cause of combat veterans accused of war crimes.