Officials hailed the new deal as a "big win for American companies and American workers".
Seoul has agreed to double to 50,000 the number of cars each US automaker can sell in the Asian nation without meeting local safety standards, said the officials, who briefed reporters on condition of anonymity.
He early on said Canada and Mexico would be exempt while the U.S. negotiates with them to revise the North American Free Trade Agreement.
The quota will be product specific and equivalent to 70 percent of the average annual export volume based on the last three years' average.
South Korea's top trade negotiator said Monday that the revised agreement calls for delaying the earlier agreed-to elimination of tariffs on South Korean-made pick-up trucks to 2041 from 2021. Numerous details of the revised trade deal and the steel quota were previously disclosed by South Korea.
The deal also will establish a side agreement between the United States and South Korea which is meant to deter "competitive devaluation" of both countries' currencies - which can artificially lower the cost of imports purchased by consumers - and to create more transparency on issues of monetary policy.
Under the new deal negotiated by the Trump administration, the US will extend a 25 percent tariff on imports of pickup trucks to the USA until the year 2041.
On automobiles, the biggest source of trade tensions between the countries, the negotiation delivered modest victories that were likely to be greeted by US carmakers that have long sought to sell more cars in South Korea. No US automaker sold more than 11,000 cars in South Korea a year ago.
One official said it was "not a one-size fits all kind of thing" and added that the South Korean quota was agreed due to its "unique" position in steel exports. The revised agreement does ease environmental regulations that USA carmakers face when selling vehicles in South Korea and makes US standards for auto parts compliant with South Korean regulations.
"The U.S. market is basically open", Schott said.
According to Trump administration officials, Washington made only minor concessions to South Korea, updating procedures for trade remedy cases and changing language on the resolution of investor-state disputes to deter frivolous or duplicate claims.
The 10 percent tariff on aluminum imports Trump announced this month will remain in place, however. One official said the changes will "create a suite of outcomes that are going to make it a lot easier for our auto companies to compete on a level playing field there in Korea".
During the meeting, Kim committed to denuclearisation in Korea if the United States and the South showed "goodwill", it was reported, with China agreeing to support its neighbor if nuclear tensions could be eased. The U.S. Department of Treasury has been conducting negotiations with Korea's Ministry of Strategy and Finance on "robust provisions that will: 1 - prevent competitive devaluation of currency, and 2 - ensure that there are commitments on transparency and accountability to make sure that countries know what others are doing with respect to monetary policy".
In addition, Korea has agreed to eliminate some regulatory barriers for USA auto exporters.