The International Monetary Fund said it had now approved the countries under a scheme launched by the Group of Eight powers, after previously saying it wanted one last "spot check" of their economic policies.
"This is an historic moment which will allow these countries to increase spending in priority areas to reduce poverty, promote growth and to make progress towards achieving the (UN) Millennium Development Goals," IMF chief Rodrigo Rato said in a statement after a Fund board meeting.
The Group of Eight powers in July announced their plan to cancel the debts of 18 of the poorest countries owed to the World Bank, the IMF and the African Development Bank.
The IMF added two countries to the G8 list, Cambodia and Tajikistan, but dropped one, Mauritania, where the military seized power in an August coup.
The IMF hopes to restore Mauritania to the list in the coming months.
Dictator’s loans
The G8 hopes the world's poorest nations can free up much-needed funds for health, education and infrastructure, once they secure relief from un-payable loans run up over decades by often corrupt and dictatorial leaders.
Their promises have come after a concerted debt-relief campaign in recent years fronted by, among others, U2 lead singer Bono.
Time magazine last weekend named the Irish rock star one of its "Persons of the Year" for having "charmed and bullied and morally blackmailed the leaders of the world's richest countries" into forgiving the debts of the poorest.
The 19 countries set to benefit are Benin, Bolivia, Burkina Faso, Cambodia, Ethiopia, Ghana, Guyana, Honduras, Madagascar, Mali, Mozambique, Nicaragua, Niger, Rwanda, Senegal, Tajikistan, Tanzania, Uganda and Zambia.
The G8 has identified an additional 20 countries that are in line for debt cancellation, taking the total that would be erased to about 57 billion dollars.
But a leaked memo by IMF staff that was submitted to the board meeting warned that Ethiopia, Madagascar, Mauritania, Nicaragua, Rwanda and Senegal must enact more economic reforms before they can win debt relief.
Activists concerned
The memo redoubled the fears of activists who had been warning for more than a week that the IMF, instead of delivering on the G8 promise to the world's neediest nations, was preparing to foist unpopular economic policies on them.
In a letter to Rato Friday, six US lawmakers from both the Republican and Democratic parties said they were "deeply concerned that the IMF is now back-tracking on this commitment" made at a G8 summit in July.
IMF spokesman Thomas Dawson said the IMF board had given in-depth study to each of the 19 recipients but dismissed the speculation of a U-turn as "simply not true".
He said the A$4.5 billion in debts owed by the 19 nations will finally be cancelled once the IMF has the approval of all 43 rich countries that have contributed to an anti-poverty trust set up by the Fund.
"So far we have 37 consents. We're quite hopeful we'll get the remaining six in the next few weeks," Mr Dawson said.
Campaign organisations said the IMF had been forced to climb down.
"It's good that the IMF realised that they couldn't wriggle out of promised debt cancellation during a closed-door session in Washington DC," Oxfam policy advisor Max Lawson said.
"The IMF must now deliver the funding quickly and without any further delay."
Neil Watkins, the national coordinator of Jubilee USA, said: "Pressure from debt campaigners across the US and the globe and supportive governments led to this important reversal."