Lymphatic filariasis (LF), often called elephantiasis, is caused by parasitic worms and causes grotesque swelling of the limbs, breasts and genitals.
A World Health Organisation-sponsored drive has delivered 1.9 billion doses of a simple cure since 2000.
Pharmaceutical firms have offered drugs free, keeping costs minimal. The success of the programme was highlighted in a paper in the Public Library of Science Neglected Tropical Diseases journal.
The Global Programme to Eliminate LF has so far prevented an estimated 6.6 million children from catching the condition, and stopped it from progressing in another 9.5 million people who already have it.
It is thought to be the most rapidly expanding drug administration programme in public health history.
Professor David Molyneux, from the Liverpool School of Hygiene and Tropical Medicine, and the Executive Secretary of the campaign, said that the success of the project was "staggering".
"In some countries we are talking about costs of five pence per person, per year.
"We are reaching hundreds of millions of the world's poorest people, and it's the additional benefits these drugs bring which are really important.
"I think that compared to most other public health programmes, it's going remarkably well."
Dr Mwele Malecela, who chairs the programme, said: "We are on track to accomplish our goal of elimination by 2020.
"When we do, this programme will be a leading case study for how to scale up disease elimination programmes globally".
There are 83 countries in the world where the disease is endemic, and the programme has so far administered treatments in 48 of them, to more than 570 million people.
The scale of the challenge is immense - approximately one fifth of the world's population, or 1.3 billion people, is said to be "at risk" of contracting LF, BBC reports.
The treatment uses a combination of two drugs, both donated free of charge from GlaxoSmithKline and Merck and Co.
These need to be given once a year for five years to ensure that the disease does not spread.
Another benefit of the drugs is that they also tackle intestinal worms, and approximately 100 million children and women have been treated for these.