Under the agreement, the automakers will pay $100 million in fines and forfeit an estimated $200 million in greenhouse-gas emissions credits, which auto companies earn by building vehicles with lower emissions than are required by law. The E.P.A. said the fuel efficiency standards reported by Hyundai and Kia were off by one to six miles per gallon.

For years Hyundai and Kia built their brands around the idea that their cars got better mileage than their competitors, a claim they promoted in ads that denigrated less efficient rivals.

But in 2012, Hyundai and Kia, which are both owned by the Hyundai Motor Group, acknowledged that they had overstated the fuel economy of vehicles sold in the United States over the previous two years. The admission came after an E.P.A. investigation into consumer complaints that their cars were underperforming the official mileage estimates on the window stickers of new cars. Although few drivers achieve the mileage claimed on the stickers, the government requires automakers to conduct standardized tests to calculate the figures so that buyers can more easily compare the fuel efficiency of different models.

At the time, both Hyundai and Kia apologized for what they called “procedural errors” in testing that resulted in incorrect mileage stickers on some of their most popular models, including the Hyundai Elantra and Kia Rio. On Monday, the companies continued to say that the misstatement of fuel mileage was inadvertent and that they did not intentionally mislead customers.

“Hyundai has acted transparently, reimbursed affected customers and fully cooperated with the E.P.A. throughout the course of its investigation,” David L. Zuchowski, president and chief executive officer of Hyundai Motor America, said in a statement. “We are pleased to put this behind us, and gratified that even with our adjusted fuel economy ratings, Hyundai continues to lead the automotive industry in fuel efficiency and environmental performance.”