More than 10,000 'alien' species have gained a foothold in Europe, from Asian tiger mosquitoes to North American ragweed, and at least 1,500 are known to be harmful, the European Environment Agency (EEA) said.
"In many areas, ecosystems are weakened by pollution, climate change and fragmentation. Alien species invasions are a growing pressure on the natural world which are extremely difficult to reverse," said Jacqueline McGlade, head of the EEA.
Introduced species that suddenly thrive in a new home in Europe, including parakeets from Africa or water hyacinth from the Amazon, were estimated to cost Europe at least €12 billion a year, according to the 118-page study.
"Our number is an underestimate," said Piero Genovesi, a lead author at the Italian Institute for Environmental Protection and Research, adding that it omitted the impacts of many species such as tropical ‘killer algae’ in the Mediterranean.
"The problem has exploded in the last 100 years," he said. Europe had the most data but the problem was worsening worldwide, he said. And more travel, trade and climate change were likely to aggravate the invasions.
"Invasive species pose greater risks than previously thought for biodiversity, human health and economies," the EEA said.
It urged more focus on preventing the arrival of unwanted species and a better early warning system to sort out the good from the bad. Many introduced species, like potatoes from South America, bring enormous benefits.
Invasion of the tiger mosquitoes
Among invaders, the tiger mosquito, native to Asia, transmitted dengue fever and was linked to an outbreak of the chikungunya virus in Italy in 2007. And climate change meant the mosquitoes were likely to spread.
Ragweed, originally from North America and spreading north in Europe in a warming climate, added to health problems since 10-20% of patients who suffered from pollen allergy suffer from ragweed.
Invasive species have been around for a long time. Pliny the Elder wrote in 77 AD that Roman troops were deployed to try to rid the Balearic islands in the Mediterranean of invasive rabbits brought from the mainland.
And European species have in turn been damaging elsewhere, such as rabbits that have spread across Australia.
Many alien invasive species were introduced deliberately and then escaped or spread rapidly - such as farmed mink from North America or ornamental rhododendron plants from Asia.
Others came accidentally, such as zebra mussels attached to ships from the Black Sea in the 19th century that choke water intake pipes at power plants or factories.
Britain eradicated the coypu, a large rodent from South America whose burrows can undermine riverbanks, in a €5-million campaign. In Italy, a bigger coypu infestation causes damage of up to €12 million a year.
The study also urged better assessment of fast-growing species before they are used as biofuel crops - such as the Japanese knotweed that can grow 30 cms (1 ft) a day and threatens slower-growing plants by blocking sunlight.