The test could transform tracking of the disease where shortages of healthcare workers and laboratories have been making an impact.
The WHO issued an emergency-use listing last week for the antigen-based rapid diagnostic tests which cost $5 dollars (£3.90) each.
The programme initially requires $600 million (£467 million) and is to get started as early as next month.
The rapid tests look for antigens, or proteins found on the surface of the virus.
They are generally considered less accurate - though much faster - than higher-grade genetic tests, known as PCR tests.
PCR tests require processing with specialised lab equipment and chemicals. Typically that turnaround takes several days to deliver results to patients.
WHO director-general Tedros Adhanom Ghebreyesus hailed the programme as "good news" in the fight against Covid-19.
"These tests provide reliable results in approximately 15 to 30 minutes, rather than hours or days, at a lower price with less sophisticated equipment," he said.
"This will enable the expansion of testing, particularly in hard-to-reach areas that do not have lab facilities or enough trained health workers to carry out PCR tests.
"We have an agreement, we have seed funding and now we need the full amount of funds to buy these tests."