The vote clears the final legislative hurdle for the deal and paves the way for the government to pay off creditors that rejected Argentina's efforts to restructure its mountain of defaulted debt.
After nearly 15 hours of debate, the deal passed with 54 votes in favor and 16 against. That seals the agreement, which passed the lower house two weeks ago.
Conservative President Mauricio Macri's administration has called the deal bitter, but necessary, to end the country's status as a pariah on international capital markets.
Buenos Aires persuaded nine out of 10 of creditors to write down 60 to 70 per cent of the face value of their bonds, but lost a lawsuit in US federal court to hedge funds demanding full payment.
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After years of combative relations with the holdouts -- dubbed "vultures" by former president Cristina Kirchner -- Macri promised to settle the dispute after taking power in December.
His more conciliatory approach is part of a broader push to reverse the slowdown of Latin America's third-biggest economy.
The new bill allows the government to issue $12.5 billion of bonds to settle with the two US hedge funds that sued it, as well as other holdouts.
Those two -- Aurelius Capital Management and billionaire speculator Paul Singer's NML Capital -- settled for a total of USD 4.65 billion.
The USD 12.5 billion will be one of the largest debt issues by a developing country in two decades.
The bill's initial passage in the lower chamber of deputies was a major victory for Macri, who had to win opposition votes in a Congress where his party lacks a majority.
Nearly half its senators reportedly caved in to pressure from the governors of their provinces, who need loans to fund infrastructure projects.