The Non-Native Species Secretariat (NNSS) described invasive species as plants that had been introduced (deliberately or accidentally) by humans since the last ice age, which were having a detrimental impact on the economy, wildlife or habitats of Britain.
It added that a recent study carried out in England showed that there were 2,721 non-native species living in
England, of which the majority (1,798 or 66%) were plants.
A report in 2000 in Scotland found a minimum of 988 species, of which 70% were plants, it observed.
Defra said that the plants listed in the ban have been sold and planted in garden ponds but have escaped into the wild taking, overwhelming native species.
Because the plants had no natural controls in the habitat, there was little to limit the spread of the plants.
As a result, the plants formed dense mats in water, depleting oxygen and light availability, causing declines in the numbers of fish and other aquatic species.
As well as being a threat to native species, the NNSS said invasive non-native aquatic weed plants also contributed to increased flood risk and damaged structures such as bridges.
"We've recommended retailers not to sell these five plant species, in some instances, for at least a decade," said Keith Davenport, chief executive of the Ornamental Aquatic Trade Association.
"So this is welcome news from Defra, making it very clear there is now a ban in place. We will continue to actively encourage our members to support the Be Plant Wise campaign."
Chris John, national ecologist at the Canal & River Trust, described the ban as the correct decision.
"Our waterways are unique wildlife corridors, home to huge variety of animals and plants, to which non-native invasives can cause all sorts of problems," he told BBC News.
"They grow rapidly, choking up canals and rivers, which affects some of our best wildlife spots and creates problems with navigation.
"As a charity, we spend a considerable amount of time and effort managing these outbreaks and the ban on sale will help reduce the chance of their reintroduction."
Carrie Hume, head of conservation policy for the Wildfowl and Wetlands Trust said: "Thankfully, some of the most destructive non-native plants will no longer be on sale in our garden centres.
"This is the right move - the environmental and economic cost of dealing with this problem is already huge and dealing with it now is a great saving for the future."
The ban means that all retailers will now have to stop selling these plants or face a fine of up to Â£5,000 and possibly up to six months in prison.
Although details of the ban have been announced now, it will not come into force until next spring to give retailers enough notice to conform to the new measures and identify and stock alternative plants.