Environment minister Richard Benyon said the ban, which comes into force in April 2014, aimed to protect wildlife. The plants are water fern, parrot’s feather, floating pennywort, Australian swamp stone-crop (New Zealand pygmyweed), and water primrose.
"Tough laws to curb the sale of these plants could save the country millions of pounds as well as protect wildlife such as fish and native plants," he said. "But as well as saving money and protecting wildlife the ban will also help maintain access to rivers and lakes for anglers and watersport fans."
Defra said in the past the plants had been sold and planted in garden ponds, but escaped into the wild taking over from native species and damaging some of our most sensitive habitats.
"The plants form dense mats in water, depleting oxygen and light availability, causing declines in the numbers of fish and other aquatic species. They also reduce access to waterways for boating and angling and increase flood risk which, taken together, can cost millions of pounds per year.
"The ban means that all retailers will now have to stop selling these plants or face a fine of up to £5,000 and possibly up to six months in prison. Retailers have a year to adjust to the ban."
Invasive non-native species could have a devastating cost to the economy, costing £1.7 billion to control, warned Defra. Floating pennywort, which can grow up to eight inches a day, cost the British economy £23.5 million per year.
"Defra, trade representatives and conservation bodies have also been working to raise awareness of garden owners and horticulturalists to the dangers of spreading non-native species through the Be Plant Wise campaign and have given widespread support to the ban."
Ornamental and Aquatic Trade Association chief executive Keith Davenport said: "We’ve recommended retailers not to sell these five plant species, in some instances, for at least a decade.
"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."
Wildfowl & Wetlands Trust’s head of conservation Policy Carrie Hume 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."