According to two people briefed on the settlement, Volkswagen is expected to plead guilty to charges of conspiracy to commit wire fraud and to violate the Clean Air Act, customs violations, and obstruction of justice. The people could not talk publicly about the deal because it was not yet final. Many of the 600,000 cars in the United States equipped with the emissions-cheating software were imported from Germany or Mexico.

The $4.3 billion in fines covers criminal and civil aspects of the government’s case, including environmental and customs-related penalties. The fines would bring the total cost of the scandal to Volkswagen in the United States to $20 billion, including settlements of civil suits by car owners, certainly one of the most costly corporate scandals in history.

The details of the deal, which requires the approval of the company’s management and supervisory boards, were provided by Volkswagen in a financial disclosure on Tuesday. Volkswagen said in the disclosure that money it had set aside for scandal-related costs would be insufficient to cover the latest agreement. A vote on the matter could come on Wednesday.

The Justice Department declined to comment.

Regulators in the United States began investigating Volkswagen in early 2014 after a study by West Virginia University showed that its diesel cars polluted far more on the road than during official emissions tests.

Company executives knew that the cars were programmed to recognize when they were being tested and to deliver exemplary pollution readings, according to investigators. Rather than admit wrongdoing, Volkswagen representatives provided false and misleading information for more than a year to the California Air Resources Board and the Environmental Protection Agency.