Speaking in Washington, Mr Trump said: "I am pleased to announce that we've just reached an agreement with Canada and Mexico, and we will be sending our product into those countries without the imposition of tariffs or major tariffs".
Canada has also agreed to drop all of its retaliatory measures and legal actions at the World Trade Organization.
In a joint statement Friday, Canada said it will lift retaliatory duties on USA products as part of the deal, which will take effect within two days.
The White House on Friday said it would hold off on deciding whether to impose steep tariffs on cars entering the U.S., delaying a major escalation that was expected to raise the price of vehicles by thousands of dollars.
Iowa farmers were among the casualties of Mexican retaliatory tariffs, which cut deeply into US agricultural exports. In fact, the Canadians and Mexicans did go along previous year with a revamped regional trade deal that was to Trump's liking.
"Now that we've had a full lift on these tariffs, we are going to work with the United States on timing ratification" of the U.S. -Mexico-Canada Agreement (USMCA), Canadian Prime Minister Justin Trudeau said Friday afternoon.
But Canada has stood firm with the USA on one key, related point: it has steadfastly refused to agree to quotas or other limits on its exports in order to get the tariffs lifted.
Canadian sources have described the idea of a quota system as a non-starter and a concession that Canada was not prepared to make.
The agreement says the US and Canada will establish a process for monitoring steel and aluminum trade between them.
The reported cited statistics that US-owned companies' share of the USA automobile market has declined from 67%, or 10.5 million units produced and sold in the United States, in 1985 to 22%, 3.7 million units produced and sold in the United States, in 2017.
The delay comes as the administration faces a deepening trade war with China even as the two sides continue negotiations for a trade deal.
The leaders of the countries signed off on the USMCA earlier this year.
Citing Ross's conclusions, Trump pointed to a doubling of U.S. imports over the last 34 years but accused Europe and Japan of raising "significant barriers" to accepting American exports in return.
The legislatures in the US, Canada and Mexico still need to approve the agreement before it can take effect.
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Supporters of his tariffs argue that they have resulted in major factory investments and more than 10,000 steel and aluminum jobs being created or saved. Canada has said that the deal will not be ratified so long as the tariffs are in place.
In monitoring for surges, either country may treat products made with steel that is melted and poured in North America separately from products that are not.