Eight others, including Nicaragua, Chad and Malawi, are expected to qualify by Christmas.
He said that all debt payments to the UK from 41 of the world's poorest countries, amounting to over £1bn, had either now been stopped, or would be held in trust for the day they can be returned to fund poverty reduction.
Mr Brown told a Drop The Debt rally organised by Jubilee 2000 in London's Trafalgar Square: "Because poverty is so great and the need so urgent, neither you nor I want the richest countries to benefit any more from the debts of these poorest countries.
"So I can say to you - and to all 41 countries on behalf of the British Government - I will renounce our right to receive any benefit from the historic debt owed by all the 41 most indebted countries."
Countries in conflict
Cameroon, Tanzania and Mozambique are among 12 countries that have, during the last year, met certain key requirements set out by the government to have their debts cleared.
Eight others, including Nicaragua, Chad and Malawi, are expected to qualify by Christmas.
The commitment made by the International Monetary Fund and World Bank to these countries will lead to over £600m in debts to the UK being written off - benefiting 200 million people.
But 21 other countries have failed because they are still involved in violent conflict or have not shown sufficient commitment to reducing poverty, improving the health and education of their people, or instituting democratic reforms.
For these countries, the chancellor said that Britain would now backdate 100% debt relief with immediate effect, and all payments would be held in trust for the day they become eligible for debt relief.
He also called for a "a new global alliance
of governments and civil societies" to make "a reality of the virtuous circle of debt reduction poverty relief and sustainable development".
On Saturday Financial Secretary Stephen Timms was travelling to Zambia, Malawi and then South Africa to explain the new initiative and talk to leaders about debt relief.
Celebrity support
Thousands of campaigners, including Live Aid founder Bob Geldof, attended Saturday's Drop the Debt rally, calling on wealthy countries to step up their actions to ease the burden of debt on the world's poorest people.
Mr Geldof praised the chancellor's initiative, and said: "It means Britain absolutely leaps ahead of other countries on a moral platform."
The rally comes just weeks before the end-of-year deadline for the cancellation of all unpayable Third World debt, set by Jubilee 2000 on its foundation in 1996.
Creditor nations agreed at last year's Cologne Summit to scrap £78bn owed them by poor countries, but so far only about £8bn of this has actually been written off.
It is thought the 52 countries in most urgent need of relief still owe a total of £268bn and Jubilee 2000 believes up to £214bn needs to be written off to end the crisis.
Saturday's event forms part of the run-up to a lobby of the G7 summit of industrialised nations in Genoa, Italy, next July, at which the group will urge wholesale scrapping of debts.
Drop the Debt leader Adrian Lovett believes the summit could be the big breakthrough the group hopes for.
"I'm asking everyone who cares about fairness and justice to join with us in a huge push to persuade the world's leaders to Drop the Debt."
But the United Nations has warned that debt relief is not enough to help some of the world's poorest countries, most of which are in Africa.
As well as dropping third world debt, it has urged rich countries to double their foreign aid and to open their markets to exports from poor countries.
The 41 countries are:
Angola; Benin; Bolivia; Burkina Faso; Burundi; Cameroon; Central African Republic; Chad; Democratic Republic of Congo; Republic of Congo; Ivory Coast; Ethiopia; Gambia; Ghana; Guinea; Guinea-Bissau; Guyana; Honduras; Kenya; Laos; Liberia; Madagascar; Malawi; Mali; Mauritania; Mozambique; Burma; Nicaragua; Niger; Rwanda; Sao Tome and Principe; Senegal; Sierra Leone; Somalia; Sudan; Tanzania; Togo; Uganda; Vietnam; Yemen and Zambia.