The new deal, reached just before a midnight deadline imposed by the U.S., will be called the United States-Mexico-Canada Agreement, or USMCA.
USA and Canadian negotiators have been working around the clock this weekend to make a Sunday midnight deadline that would allow the countries to sign the deal before Mexico's outgoing President Enrique Pena Nieto leaves office on November 30.
Canada's ambassador to Washington says the USA and Canada have made a lot of progress in free trade talks but there is no deal.
The two sides are discussing the last sticking points, including greater market access for USA supplies into Canada's dairy market, according to the people, who spoke on the condition of anonymity because the discussion are private.
Sunday morning, Peter Navarro, one of Trump's closest White House trade advisers, said negotiators were working "in good faith" to reach a three-country deal by midnight and had reached "broad agreement" on most issues.
If a Nafta deal is reached, the USA government would see little reason to impose auto tariffs on Canada, though it was unclear whether there would be any hard exemption granted, some of the people said. He blames the treaty for the loss of American manufacturing jobs and has repeatedly threatened to abandon the trade past signed in 1994, during the Clinton administration.
But with an overnight deadline approaching, negotiators reached a deal which the two countries said would "result in freer markets, fairer trade and robust economic growth in our region". Pierre Lampron, president of Dairy Farmers of Canada, said in a statement.
The trade imbalance would change, Trump said in June during a press conference at the Group of Seven (G7) summit in Canada.
Canada is also reported to have secured some protections for automobile industry against potential U.S. tariffs.
Key U.S. lawmakers have called for the three-nation format to continue, meaning Congress may delay a new agreement that doesn't include its northern neighbour.More news: TV Ratings Are Out For Tiger Woods’ Final Round On Sunday
After months of sputtering talks, momentum picked up this weekend as Trudeau inserted himself and made clear that he wanted to get something done.
So-called Chapter 19 dispute panels, which the US wants to eliminate from Nafta and which Canada wants to preserveAn exemption for cultural sectors which Canada wants to preserveThe use of Section 232 investigations to apply tariffs to steel, aluminum, and potentially cars.
Ottawa and Washington remained at odds over Canada's subsidized dairy sector, and the dispute resolution provisions in NAFTA.
Political deadlines are often fuzzy but Canada and the United States appear to be working towards some major compromises and a NAFTA deal.
Lawmakers from both parties have urged the White House to include Canada in any revised Nafta, warning that excluding Canada, which is America's largest export market, could disrupt supply chains, cost jobs, and slow the U.S. economy. One of the officials said the discussions between Canada and the USA were ongoing, but progress was being made.
"It's a good day for Canada", said Prime Minister Justin Trudeau as the meeting wrapped up just over an hour after it started.
The official says the agreement preserves a NAFTA dispute-resolution process that the US wanted to jettison.
Daniel Ujczo, a trade attorney with the Dickinson Wright law firm who has followed the talks closely, said he expects the USA to get more access to the Canadian dairy market.
Under the current system, USA imports exceeding quota levels are subject to excessively high tariffs, such as 245 percent for cheese and 298 percent for butter.
Under the deal signed with Mexico in August, 75 percent of auto content will be made in the United States or Mexico, up from the original threshold of 62.5 percent.
Both Ujczo and Hassan Yussuff, the head of the Canadian Labour Congress and a member of the federal government's NAFTA advisory council who was also briefed on the talks Sunday, say the question of how to deal with the 232 tariffs remains the central issue.