From 12 January, visitors from countries which do not need visas will need to fill in an electronic form at least 72 hours before they travel.
Those who have not registered risk being detained and sent back home.
The Foreign Office fears some people do not know about it and critics say it might put people off visiting the US.
The new online registration scheme replaces the green I-94 forms that people on short term visits to the US had to fill in on the flight and hand to customs on arrival.
America welcomes nearly 60 million tourists a year and about 50 million of those travel without the formality of a visa.
Britain is one of the countries that signed up to the visa waiver programme, but from Monday, new rules apply.
Electronic applications – known as Esta (Electronic System for Travel Authorisation) – have to be approved by the US Department of Homeland Security.
Once an application is approved, it will be valid for all visits to the US for a two-year period.
The US Embassy in London said so far 99.6% of the applications have been approved – most within four seconds.
Michael Restovich, from the US Department of Homeland Security, said: “We want to keep the bad people out. We don’t want to restrict commerce, we don’t want to restrict tourism.
“We want to make sure the people getting on that aircraft or that sea vessel are clear to come to the United States and are risk-free.”
The Foreign Office said it was “particularly concerned that people who may not have heard of Esta and booked their trip before enforcement of the new rule may be caught out”.
Andrew Spice, of Post Office Travel Services, said: “Problems may also occur if UK tourists travel to the US via another country – like Canada or the Caribbean Islands – and don’t realise they will need the Esta to gain entry.”
Neal Weston from the British Air Transport Association, which represents UK-registered airlines, such as British Airways and Virgin Atlantic, said its members who fly to the US were fully prepared for the new system.
Abta – the Travel Association – believes it will help speed up the immigration process.
Frances Tuke, from Abta, said it had been reminding members about the Esta deadline for several months.
“We would advise people thinking about going to the US to fill in Esta before booking or as soon as they book because if it is rejected, it can take up to six weeks to get an appointment at the US embassy for a visa,” she said.
She recalled British singer Yusuf Islam, formerly known as Cat Stevens, who was sent back to London from the US after his name was found on a “watchlist” in 2004, and said the new system should help prevent such incidents.
Esta is free but she warned that searches for Esta online brought up numerous websites offering to process the application in return for personal details and a fee.
Critics say it will be an inconvenience for business travellers and could prove a disincentive to people who like to travel spontaneously and book last-minute weekend breaks to US cities.
Simon Calder, travel editor of the Independent, said: “There are many, many draws the United States has but with an extra layer of very intrusive bureaucracy, I think a lot of people will be deterred, if not simply confused.”