Mr Trudeau said the deal was a major step for Canada's economy but warned that there is more work to be done.
The signing of the U.S. -Mexico-Canada agreement, or USMCA as Trump refers to it, comes a day before Mexican President Enrique Pena Nieto's successor is set to be sworn in to office.
Mr Pena Nieto, who will be replaced on Saturday with Mexico's newly-elected president, has sold the deal to his people as a victory, saving free trade from a U.S. president who wanted to see it killed.
US tariffs on Canadian steel and aluminum will remain in place for the time being, Freeland's office has confirmed.
The new version comes after more than a year of negotiations and numerous details were agreed earlier this year - in August between the United States and Mexico and at the end of September between the USA and Canada.
Meanwhile, Mr Trump's other major trade-related meeting during the G20 summit will be with China's leader Xi Jinping on Saturday, with analysts looking for any sign that the United States president will hold off on plans to toughen USA tariffs on Chinese imports in January.
Turkey could play 'mediator role' in Russia-Ukraine crisis: Erdogan
Russia annexed the Crimean Peninsula in March 2014, claiming its ethnic Russian majority was under threat from the Ukrainian government.
Among other things, the agreement also lengthens copyrights for creative works and patent protection for certain sophisticated medicines, slightly opens up the protected Canadian dairy industry to US access and eliminates the long-controversial "Chapter 11" provision between Canada and the USA allowing investors to sue governments for allegedly violating their rights.
Trump, who arrived in Buenos Aires late Thursday, barreled into the two-day meeting by announcing via Twitter that he was canceling a planned meeting with Russian President Vladimir Putin over Russia's seizure of Ukrainian vessels.
It was unclear what exactly the three countries would sign.
"That's bad news for a lot of us", said Rufus Yerxa, president of the National Foreign Trade Council, which represents multinational corporations. He struck a more optimistic note on Friday, saying, "It's been so well-reviewed, I don't expect to have very much of a problem".
But the path to Friday's signing has been bruising, and those sore spots will be impossible to ignore when the three countries' leaders gather to talk trade for the first time since 13 months of talks culminated in an 11th-hour agreement late in September. "The fact that this is an agreement in three languages adds to the level of technical complexity and it is on that level that we are just being sure that all the Is are dotted and all the Ts are crossed". To placate critics of the original NAFTA negotiated under Republican president George H.W. Bush, Democratic president Bill Clinton negotiated "side letters" adding some new provisions. Posing for photos in the gilded Salón Blanco, Trump spoke about their longtime personal relationship and said they would discuss trade, military purchases and other issues. "It's great for all of our countries".