Tighter measures have also been brought in by Italy, Japan, Malaysia, Taiwan and India.
After almost three years of restrictions, China will let people travel more easily from 8 January.
At the same time, the country is facing a surge in Covid cases, leading to wariness among some countries.
However, Beijing said coronavirus rules should be brought in on a "scientific" basis, and accused some countries and media of "hyping up" the situation.
The UK government says it had no plans to re-introduce testing or other entry requirements for travellers.
On Monday and Tuesday, China announced it would ease its restrictions on travel to and from the country.
From 8 January, quarantine for travellers entering China will end, and passport applications for Chinese citizens will resume, authorities said.
Travel sites reported a spike in traffic following the announcements - and some countries revised their travel rules.
The US said that from 5 January all passengers travelling from China, Hong Kong and Macau would need a negative Covid test to enter the country in order to "slow the spread" of the virus.
A US department of health statement said air passengers would need to take a Covid test no more than two days before departure. It added that those who tested positive more than 10 days before the flight could provide documentation of recovery from Covid instead of a negative test result.
The measures applied to people flying via a third country and to passengers taking connecting flights through the US to other destinations, it said.
It said it would "continue to monitor the situation" and adjust its approach "as necessary".
It also accused China of failing to provide "adequate and transparent" Covid data, which it said was "critical" for monitoring infection surges "effectively" as well as decreasing the chances of new variants emerging.
The true toll of daily cases and deaths in China is unknown because officials have stopped releasing the data. Reports say hospitals are overwhelmed and elderly people are dying.
But earlier on Wednesday, Wang Wenbin, China's foreign minister spokesman, accused Western countries and media of "hyping up" and "distorting China's Covid policy adjustments".
He said China believed all countries' Covid responses should be "science-based and proportionate", and should "not affect normal people-to-people exchange".
Mr Wang called for "joint efforts to ensure safe cross-border travel, maintain stability of global industrial supply chains and promote economic recovery and growth".
The European Commission said its health security committee will convene on Thursday to discuss "possible measures for a coordinated EU approach" to China's Covid situation.
But EU member state Italy - once the global epicentre of the virus after it spread from China in late 2019 and 2020 - has already imposed restrictions on people arriving from China.
It said it was bringing in mandatory Covid testing for all passengers coming from China.
Health Minister Orazio Schillaci said this was "essential to ensure the surveillance and identification" of any new variants of the virus, and to "protect the Italian population".
Before his announcement, flights arriving in Milan were already testing passengers flying from China.
On one flight, which landed at the city's Malpensa Airport on 26 December, 52% of passengers were found to be positive for Covid, la Repubblica reports.
Other countries had already imposed some restrictions on travellers coming from China:
- In Japan, from Friday all travellers from China and those who visited it within seven days will be tested for Covid upon arrival, Prime Minister Fumio Kishida said. Those who test positive will be required to quarantine for seven days if they have symptoms, or five days if asymptomatic. The number of flights to and from China will also be restricted
- In India, people travelling from China and four other Asian countries must produce a negative Covid test before arriving. Passengers will be put in quarantine if they have symptoms or test positive
- Taiwan says people arriving on flights from China, as well as by boat at two islands, will have to take Covid tests on arrival from 1 January to 31 January. Those who test positive will be able to isolate at home, Taiwan's Central Epidemic Command Centre said
- Malaysia has also put additional tracking and surveillance measures in place.
Australia's Prime Minister Anthony Albanese said there would be no changes to its travel regulations for travellers from China, adding that Australia is monitoring the situation closely both in China and around the world.
In Belgium, the mayor of tourist hub Bruges called for Chinese visitors to face Covid tests or mandatory vaccine requirements.
China's loosening of travel measures - the last part of the country's controversial zero-Covid policy - follows weeks of unrest which saw people take to the streets in rare protests against President Xi Jinping and his government.