It was scrapped by ex-Chancellor Rishi Sunak at the start of last year in part because the Treasury claimed it was a tax giveaway that only benefitted London.
But critics said it would drive tourists to rival centres such as Paris and Milan where they can still claim back VAT.
But in his statement Mr Kwarteng said: “Britain welcomes millions of tourists every year, and I want our high streets and airports, our ports and our shopping centres, to feel the economic benefit. So we have decided to introduce VAT-free shopping for overseas visitors.
“We will replace the old paper-based system with a modern, digital one. And this will be in place as soon as possible. This is a priority for our great British retailers – so it is our priority, too.”
The move which combined with thew fall in the value of the pound will make London a far cheaper shopping destination, was received with enthusiasm.
Dee Corsi, interim CEO at business group New West End Company, said: “Today’s decision to reintroduce tax-free shopping for overseas visitors is a great victory for London’s International Centres.
“Now the West End can compete on a level playing field with Paris, Milan and Madrid as one of the world’s top shopping and leisure destinations.
“In 2019 international visitors contributed over £28 billion to the UK economy. The Government’s announcement is great news and – with new exciting new brands expected across the West End following today’s announcement that newly opened businesses will not be subject to business rates – we are confident that we can exceed this figure in the years to come.”
Linda Ellett, UK head of consumer markets, retail and leisure at consultants KPMG, said: “The return of VAT-free shopping for tourists increases the London’s competitiveness when it comes to attracting the spending power of international visitors.
“This is all the more key as we look to find ways to create economic growth, return international tourism to pre-pandemic volumes, and withstand rising inflation on the high street.”
Thierry Andretta, CEO of luxury goods brand Mulberry, said: “This decision will reinstate London and the other major U.K. cities to their rightful place among the top luxury shopping destinations in the world, as well as providing invaluable support to the U.K’s hospitality sector.”
Paul Barnes, chief executive of the Association of International Retail, said: “The reintroduction of tax-free shopping will give retailers across the country a much needed boost in trade as international shoppers return to the UK. It allows us to compete equally with our European neighbours to attract high spending international visitors back to our shops, hotels and restaurants.
“Today’s news brings with it a huge new tourist market of over 440 million people from the EU – now that Britain is the only country in Europe where EU visitors can shop tax free – which will be a significant shot in the arm to our retail, hospitality and tourism sectors across the country, with regional airports set to benefit from a surge in their visitor economies.
“This is a very good move by the Government, and is set to deliver swift results as international visitors return in force across the country.”