So-called "stablecoins" will become recognised forms of payment to give people confidence in using digital currencies, it said.
Stablecoins are designed to have a stable value linked to traditional currencies or assets like gold.
They are considered less volatile than cryptocurrencies such as Bitcoin.
The Treasury also said it planned to consult on regulating a much wider range of digital currencies later this year, without saying which they might be.
Chancellor Rishi Sunak said: "We want to see the [cryptocurrency] businesses of tomorrow - and the jobs they create - here in the UK, and by regulating effectively we can give them the confidence they need to think and invest long-term."
The Treasury has not yet confirmed which stablecoins will be regulated; well-known ones include Tether and Binance USD.
Stablecoins are currently used in the United States to facilitate trading, lending or borrowing of other digital assets.
However, they are not without controversy. Tether, a Hong Kong based company, has faced questions over its business practices and was fined $41m in 2021 by the US Commodities Futures Trading Commission for allegedly misstating its reserves.
The UK's Treasury said regulating stablecoins would ensure they could be used "safely" by the public.
Cryptocurrencies are virtual or digital currencies that can be traded or used to buy goods and services, although not many shops accept them yet and some countries have banned them altogether.
They are exchanged via "peer-to-peer" transactions, meaning there are no banks or other third parties involved.
Wild fluctuation in the value of some digital currencies has led regulators to warn they pose risks. However, they are increasingly going mainstream, with major financial companies now investing in them.
Meanwhile, Tesla founder Elon Musk, the richest person in the world, has voiced his support for virtual currencies and said Bitcoin is a "good thing".
Separately, the Treasury said it will ask The Royal Mint to create a Non-Fungible Token (NFT) this summer.
NFTs are assets in the digital world that can be bought and sold, but which have no tangible form of their own.
The digital tokens, which emerged in 2014, can be thought of as certificates of ownership for virtual or physical assets. NFTs have a unique digital signature which means they cannot be copied or replicated.
UK Financial Services Minister John Glen said the UK saw "enormous potential in crypto" and had a "detailed plan [for] harnessing the potential of blockchain and supporting the development of a world-best crypto ecosystem".
"What does the future of crypto here in the UK look like? No-one knows for sure," he said in a speech.
"But we think that by making this country a hospitable place for crypto we can attract investment [and] generate swathes of new jobs."
Regulators are racing to draw up rules to manage cryptocurrencies amid concern that their growing popularity could threaten established financial systems.
In December, the Bank of England's deputy governor said that while only about 0.1% of UK wealth was currently held as digital assets, that proportion was growing quickly.
Sir Jon Cunliffe told the BBC that if the value of cryptocurrencies fell sharply, it could have a knock-on effect.
Meanwhile, the US is moving to craft regulations amid rising concern that the cryptocurrency industry is a haven for criminals.
The process of generating digital coins via banks of powerful computers, called mining, is also highly energy intensive. Recent research suggests Bitcoin now generates carbon emissions comparable to the country of Greece.
Mr Glen admitted there were concerns about the environmental impact and said the government "will be looking closely at energy usage associated with certain crypto-technologies".