There are three direct flights a week that arrive at Heathrow Airport from Wuhan in China.
As each of these flights land, the captain will tell passengers to let a flight attendant know if they feel unwell.
These details will then be passed on to public health teams at the airport who will carry out further checks.
There are no plans to introduce blanket temperature screening of all passengers, a spokesman for the DHSC said, as the incubation period for the illness can be five days.
But all passengers on each flight will be given a leaflet explaining how they can seek help if they become unwell while in the UK.
A statement from the DHSC said: "We have been carefully monitoring the situation in Wuhan for some time and are ready to put in place proportionate, precautionary measures.
"From today, enhanced monitoring will be in place from all direct flights from Wuhan to the UK.
"The enhanced monitoring package includes a number of measures that will help to provide advice to travellers if they feel unwell.
"For those travelling back directly from Wuhan, this includes a port health team who will meet each direct flight aircraft to provide advice and support to those that feel unwell."
The move comes as Public Health England (PHE) upgraded the risk to the UK population from coronavirus from "very low" to "low".
Dr Nick Phin, deputy director of the National Infection Service at PHE, said: "This is a new and rapidly evolving situation where information on cases and the virus is being gathered and assessed daily.
"Based on the available evidence, the current risk to the UK is considered low.
"If you are travelling to Wuhan, you should maintain good hand, respiratory and personal hygiene and should avoid visiting animal and bird markets or people who are ill with respiratory symptoms.
"Individuals should seek medical attention if they develop respiratory symptoms within 14 days of visiting Wuhan, either in China or on their return to the UK.
"They should phone ahead before attending any health services and mention their recent travel to the city."
Chinese authorities have told people to stop travel into and out of Wuhan.
There have been 440 confirmed cases, according to official Chinese figures, and nine people have died.
A handful of cases have been identified abroad, including in Japan and the US, but there have been no reported cases in the UK.
Symptoms of coronavirus can include fever, cough, shortness of breath and breathing difficulties.
Later on Wednesday, the World Health Organisation (WHO) will decide whether to declare an international public health emergency over the virus.
Peter Horby, professor of emerging infectious diseases and global health at the University of Oxford, said: "It's a respiratory virus, it's most transmitted through the respiratory route.
"With most of these viruses, transmission is predominantly through droplets."
Neil Ferguson, director of the Medical Research Centre for Global Infectious Disease Analysis, said the estimated number of people infected with coronavirus in Wuhan is around 4,000, with a range between 1,000 and 9,700.
Of the new enhanced monitoring of passengers on flights, he said: "This sort of measure of trying to identify people who are sick coming off a plane will only identify, if you're lucky, people who will have fever coming off a plane.
"If somebody was infected two days before they travelled, they will arrive without any symptoms at all.
"That's why it's essential that actually the entire... health system is alert to the possibility of imported cases.
"And there is a protocol in place now whereby if somebody reports with moderately severe respiratory symptoms to their GP or hospital and reports a travel history to Wuhan, or to the area, then Public Health England will be alerted of that case.
"It's understandable countries want to try and reduce the threat by various measures at the border.
"But the border will still be porous."