Official reports say there have been nearly 30,000 cases globally and 141 deaths, with figures rising daily.
Hong Kong said it was closing all its nurseries and primary schools for two weeks following 12 school cases.
It is the first flu pandemic in 40 years - the last in 1968 killed about one million people.
However, the current pandemic seems to be moderate and causing mild illness in most people.
Most cases are occurring in young working age adults and a third to a half of complications are presenting in otherwise healthy people.
Dr Chan said: "We have evidence to suggest we are seeing the first pandemic of the 21st Century.
"Moving to pandemic phase six does not imply we will see increased in deaths or serious cases."
She added it was important to get the right balance between complacency and vigilance and that pandemic strategies would vary between countries depending on their specific situation.
It is global and fulfilling the requirements of a pandemic
Professor John Oxford, flu expert
And the WHO does not recommend closure of borders or any restrictions on the movement of people, goods or services.
But the picture could change very quickly.
"No other pandemic has been detected so early or watched so closely," Dr Chan said.
UN Secretary General Ban Ki-moon called for calm.
"Let me stress: this is a formal statement about the geographical spread of the disease. It is not in itself a cause for alarm," he said.
He warned that in the developing world the consequences of the virus could be more serious, and that the southern hemisphere was now entering the flu season.
One factor which has prompted the move to a level six pandemic was that in the southern hemisphere, the virus seems to be crowding out normal seasonal influenza.
Pandemic 'no cause for alarm'
The move was not prompted by the situation in any one country but the reports that it had spread in several parts of the world, officials said.
The BBC's Imogen Foulkes, in Geneva, says that while the number of cases has made the declaration inevitable, the WHO will have to manage the global anxiety the declaration of a pandemic will generate.
Experts have warned that poorer nations, especially those in the southern hemisphere now heading into their winter season, face the greatest risk from the flu pandemic.
There have been more than 800 cases in the UK with some areas of Scotland being particularly hard hit.
The government has been stockpiling antivirals such as Tamiflu and has ordered vaccine, some doses of which could be available by October.
SWINE FLU - THE BASICS
Symptoms usually similar to seasonal flu
It is a new version of the H1N1 strain which caused the 1918 flu pandemic
Current treatments do work, but as yet there is no vaccine
Good personal hygiene, such as washing hands, covering nose when sneezing advised
England's chief medical officer Sir Liam Donaldson said the WHO declaration of a pandemic would not significantly change the way the UK was dealing with swine flu at the moment.
But he added there could be some minor changes to who received antivirals.
"The declaration of a pandemic per se doesn't make a big difference to the way we are handling the outbreaks we have.
"We are going to continue to investigate every case that occurs and treat their contacts with antivirals even though they may not be ill.
"The difference is that the Health Protection Agency has learnt a lot about approaching this question of antiviral prophylaxis and they are going to be treating the closer contacts of the cases, rather than the more far-flung contacts, because they feel that that is supported by what they know so far about how the disease is transmitting.
He added: "These flu viruses can change their pattern of attack, so when we come into the flu season in the autumn and winter in this country, when we expect a big surge of cases, we need to watch very carefully to see if the character of the virus is changing."
There is concern that the virus might mutate in the southern hemisphere over its winter and become more virulent, but there's no sign of that yet
Scottish health secretary Nicola Sturgeon said a move to level six means that countries need to be ready to implement pandemic plans immediately but the UK was already operating at a "heightened state of readiness".
But it could affect the speed at which the UK gets pandemic vaccine supplies but that had been factored into pandemic planning.
Flu expert Professor John Oxford said people should not panic as the outbreak was milder than others seen in the past century.
"It is global and fulfilling the requirements of a pandemic but I don't think anyone should worry because nothing drastic has happened between yesterday and today."
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