Dan Bongino, a former New York City police officer and Secret Service agent turned right-wing pundit and podcaster, will be the next deputy director of the F.B.I., President Trump said on Sunday night.

Mr. Trump, making the announcement on his social media site, said the newly installed F.B.I. director, Kash Patel, had named Mr. Bongino to the No. 2 post at the country’s most powerful law enforcement agency. The role of deputy director does not require Senate confirmation, meaning two steadfast Trump loyalists will effectively be installed at the uppermost reaches of an agency known for its tradition of independence.

The announcement came about an hour after the F.B.I. Agents Association told its members that Mr. Patel had privately acknowledged that the next deputy director should be an F.B.I. agent, intensifying mistrust among the rank-and-file.

The F.B.I. did not respond to a request for a comment.

In the past, F.B.I. directors have selected senior agents with extensive experience to essentially run the bureau’s operations, a complex and grueling job that requires working closely with foreign partners and navigating sensitive investigations.

The choice of Mr. Bongino is a radical and abrupt departure from that practice and raises startling questions about how two people who have never served as F.B.I. agents will oversee the vast surveillance and investigative powers of an agency of 38,000 people and a budget of about $11 billion.

The combination of Mr. Patel and Mr. Bongino will represent the least experienced leadership pair in the history of a bureau typically insulated from White House interference. It will also ensure that the bureau will be run by men who have freely peddled misinformation and embraced partisan politics.