And the species has swiftly been invading other countries including Spain in 2010, Portugal and Belgium in 2011, Italy in 2012 and Germany in 2014.
The invasive hornets made it to the UK in 2016 – and in December 2019, were first spotted in the U.S. in Washington.
Experts are now warning that the species will begin to swarm in spring, as the hornet's life cycle begins in April.
In a new study – published first in the journal NeoBiota – French scientists evaluated the estimated cost of this non-native hornet invasion to the U.S. and Europe.
They did so by analysing the negative impact Asian hornets have on ecosystems and the global decline in pollination and honey production.
The invasion is mainly controlled by destroying hornet nests and bait trapping.
But the authors say these methods are not enough to completely eradicate the species.
The team divided costs into three main categories - prevention of the invasion, fighting the invasion, and damage caused by the invasion.
The cost of fighting the invasion was the price of nest destruction - calculated by studying the companies that provide the service.
Research leader Professor Franck Courchamp said just two years after the hornet was first spotted in France, estimates show it cost roughly $446,000 to destroy nests.
"Since then, the estimated yearly costs have been increasing by about 450,000 euros each year (roughly $492,000), as the hornet keeps spreading and invades new departments.
Courchamp said over a ten-year period – from 2006 to 2015, the nest destruction cost more than $25 million, according to estimates.
So far, nest destruction is the most effective way to fight the invasion but experts say it is not enough to kill off the species.
Only 30 to 40 per cent of the detected nests are destroyed each year in France.
And those that are destroyed are the ones that have been deemed particularly harmful to human or beekeeping activities.
The scientists are calling for more active measures and research into the invasion of Asian hornets.
Professor Courchamp said: "The current study presents only the first estimates of the economic costs resulting from the Asian hornet, but definitely more actions need to be taken in order to handle harmful invasive species - one of the greatest threats to biodiversity and ecosystem functioning."
Experts in Washington are calling for people to take action now, so the species can be controlled before it becomes out of hand.
“As a new species entering our state, this is the first drop in the bucket,” Todd Murray, WSU Extension entomologist and invasive species specialist told Washington State University.
Murray said once invasive species take a foothold, they cause "forever changes" to agriculture and ecosystems.
“We need to teach people how to recognize and identify this hornet while populations are small, so that we can eradicate it while we still have a chance.”