Luiz Inacio Lula da Silva, Brazil's president, who stands to gain regional clout from the grouping, said that this was a sign that South America was becoming a "global actor".
'Number one enemy'
Brazil also wants Unasur to co-ordinate defence affairs across South America.
Hugo Chavez, Venezuela's president, said the association was a counterweight to the US.
"The number one enemy of the union of the south is the empire of the United States trying to generate wars in South America to divide and conquer," he said.
Lula invited other Latin American and Caribbean nations, saying: "Unasur is born, open to the entire region, born under the signs of diversity and pluralism."
However, the grouping is not without its divisions. Borja stepped down as the union's secretary-general on Thursday saying that some leaders had balked at his vision of putting regional trade blocs within Unasur's remit.
Leaders were also split over plans for a South American defence council that would resolve conflicts, promote military co-operation and possibly co-ordinate joint weapons production.
Colombia had not only opposed joining the council but had turned down the presidency because of its dispute with Venezuela and Ecuador over Farc rebels.