The International Monetary Fund and the World Bank said the country had made good efforts to reform its economy and governance in recent years.
The news comes in the same week as the country marks the 50th anniversary of its independence.
DR Congo currently pays around $300m (£198m) every year in debt repayments.
The African country has been hard hit by violence and bad governance.
An estimated 5m people died in what was dubbed “Africa’s world war” between 1998 and 2003, and areas of the country remain in conflict.
Despite having a multitude of valuable minerals, most of its citizens are poor.
Meanwhile, the United Nations mission in the country has marked the beginning of its fresh mandate by officially changing its name.
The Secretary General of the UN, Ban Ki-moon, said the main focus of the UN Stabilisation Mission in the DRC, Monusco, would be to consolidate peace.
The mission, so far known as Monuc, has been in the country since 1999.
Its new mandate expires at the end of June next year.
The country itself is among the group known by the IMF and World Bank as the Highly Indebted Poor Countries.
The debt relief plan comes under their initiative to help these countries escape their debts in return for economic and government reforms.
The new debt relief could see as much as 90% of DR Congo’s external debt erased, the BBC’s Thomas Fessy reports from Kinshasa.
But the deal was opposed by representatives from Canada and Switzerland, who voiced concerns about governance reform.
Canada had blocked the debt relief package earlier in the week amid a dispute between a Canadian mining firm and the government of President Joseph Kabila.
The government closed down a cobalt mining project run by the company First Quantum in September.
But on Thursday the international finance organisations voted the measures through, with Canada and Switzerland abstaining.