WASHINGTON — A veteran counterterror official will become President Trump’s new White House counterterrorism coordinator after the departure of a public servant who had defined the role during a stretch of the White House’s often-tumultuous response to terror threats.

John Bolton, who was confirmed as President Trump’s national security adviser on Thursday, has tapped former deputy director of the FBI, Andrew McCabe, to fill the position, according to a person familiar with the matter. Mr. McCabe will take over on April 16. The post had been vacant since last August.

Mr. Bolton, a hawkish foreign policy hawks, has a history of selecting retired military figures to serve in senior roles.

“To be very clear, this position does not require Senate confirmation,” Mr. Bolton said in a statement, naming Mr. McCabe and two other transition leaders who will also oversee the Office of the National Security Adviser, which reports to the president. “Each individual will bring great experience and knowledge to this important office.”

Mr. Bolton was chosen by the president not only to replace Mr. H.R. McMaster, the national security adviser, but also to replace Mr. Rob Porter, who resigned after several women accused him of spousal abuse.

Among Mr. Bolton’s choices is John Roth, a former deputy director of the FBI, who was nominated to serve as the Department of Justice’s new top law enforcement official on Tuesday.