The decision was announced by WHO Director-General Margaret Chan, after consulting with the global body's emergency committee of top flu experts.
"We are now moving into the post-pandemic period," Chan said. "The new H1N1 virus has largely run its course."
The number of deaths from swine flu has fallen dramatically in recent months.
Last week, WHO said at least 18,449 people had died worldwide since the outbreak began in April 2009, though it noted that the true figure is likely to be higher. Still, lab-confirmed deaths globally increased by only about 300 in the past two months.
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"As we enter the post-pandemic period, this does not mean that the H1N1 virus has gone away," Chan said. "Based on experience with past pandemics, we expect the H1N1 virus to take on the behavior of a seasonal influenza virus and continue to circulate for some years to come."
Switzerland's Office of Public Health gave local authorities permission in May to destroy expired swine flu vaccines after finding its stocks were full of unused supplies. A total of 20 people died from swine flu in Switzerland - out of almost 5,000 across Europe. That figure is far lower than the number of people who would normally die from seasonal flu every year, a fact that has been partly attributed to higher vaccination rates and some level of immunity among older people.
Prof. Angus Nicoll, flu program coordinator at the European Center for Disease Prevention and Control, said a decision to declare the pandemic over would be consistent with the Stockholm-based body's recent findings.
While flu activity in the northern hemisphere is seasonally low, monitoring in southern hemisphere countries shows that few people are falling seriously ill from swine flu, said Nicoll.
Local spikes in flu deaths, such as seen recently in India, are likely due to better surveillance, he said.
Nevertheless, health officials around the world should prepare for a new type of seasonal flu to appear in the near future that will combine elements of the pandemic A(H1N1) strain, and older A(H3N2) strain and several lesser strains, said Nicoll.
"It looks sort of middle of the road at the moment," he said.
Nicoll noted that high-risk groups such as pregnant women should continue to get vaccinated because swine flu has been shown to pose a particular risk to them.
Health authorities in Britain shut down their pandemic flu hotline in February and canceled vaccine orders by a third back in April as it became clear the pandemic strain would be less dangerous than feared. Worst-case scenarios had predicted up to 65,000 deaths in Britain. In the end there were 457 confirmed deaths from swine flu.
In Germany, authorities are meeting later this week to discuss who is going to pick up the bill for the 34 million doses of vaccines that were ordered and mostly not used.