The deal, which is now formally known as The Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), doesn't pack quite the same punch without the support of the USA, but it will still be one of the world's three largest trade agreements.
Trade supporters have said that in reality, free trade deals usually delivered much higher returns.
The Comprehensive Progressive Trans-Pacific Partnership (CPTPP) will be signed soon in this capital, amid divided opinions.
"Today, we can proudly conclude this process, sending a strong message to the worldwide community that open markets, economic integration and global cooperation are the best tools for creating economic opportunities and prosperity", said Chilean President Michelle Bachelet.
"The CPTPP will establish a new standard for other regional economic integration agreements, and even for future negotiations in the World Trade Organization and in Asia-Pacific Economic Cooperation", said Chile's foreign ministry.
In May 2017, foreign trade ministers of the Trans-Pacific Partnership (TPP) signatory countries agreed to assess the options to reach a new agreement following the United States' withdrawal.
They also welcomed the interest shown by a number of other economies wishing to join the trade bloc, which accounts for 13.5 per cent of the world's gross domestic product.
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The argy-bargy over America's proposed tariffs on steel and aluminium is set to briefly take a back seat as 11 nations sign the Trans-Pacific Partnership trade pact.
The pact will come into force 60 days after it is fully ratified by six of the 11 members.
"This is a fair deal for New Zealand", Mr Parker said after he had signed the CPTPP. The countries are Singapore, Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru and Vietnam.
Last month, Trump told the World Economic Forum in Davos that the U.S. might return if it got a better deal.
The pact, which will significantly cut import taxes on a variety of products and services traded among these countries, is being criticized by Australian unions and leftist parties Chile and New Zealand for infringing on their respective national sovereignty.
"The real worry has to be not only that our government has rolled over on this one", she added, "but that it and the other 10 will roll over to the demands of the Trump administration if they want to re-enter".
The European Union said this week that it is ready to retaliate against Trump's tariffs - of 25 percent on imported steel and 10 percent on aluminum imports - with counter-measures against iconic US products like Harley Davidson motorcycles, Levi's jeans and bourbon.