Fifteen countries have formed the world's largest trading bloc, covering nearly a third of the global economy.
The Regional Comprehensive Economic Partnership (RCEP) is made up of 10 Southeast Asian countries, as well as South Korea, China, Japan, Australia and New Zealand.
The pact is seen as an extension of China's influence in the region.
The deal excludes the US, which withdrew from a rival Asia-Pacific trade pact in 2017.
President Donald Trump pulled his country out of the Trans-Pacific Partnership (TPP) shortly after taking office. The deal was to involve 12 countries and was supported by Mr Trump's predecessor Barack Obama as a way to counter China's surging power in the region.
Negotiations over the RCEP lasted for eight years. The deal was finally signed on Sunday on the sidelines of a virtual summit of the Association of Southeast Asian Nations, hosted by Vietnam.
Leaders hope that the agreement will help to spur recovery from the coronavirus pandemic.
"Under the current global circumstances, the fact the RCEP has been signed after eight years of negotiations brings a ray of light and hope amid the clouds," said Chinese Premier Li Keqiang.
India was also part of the negotiations, but pulled out last year over concerns that lower tariffs could hurt local producers.
Signatories of the deal said the door remained open for India to join in the future.
The RCEP is expected to eliminate a range of tariffs on imports within 20 years. It also includes provisions on intellectual property, telecommunications, financial services, e-commerce and professional services.
Members of the RCEP make up nearly a third of the world's population and account for 29% of global gross domestic product.
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