The shower is the first such spectacular of the year, and should be visible all through the night.
The Quadrantids are not one of the relatively famous meteor showers, but are remarkable because they come first in the year and at a time of long nights in the UK.
But it is worth noting that the Quadrantids are partly obscure because they are a little less spectacular than some of the other meteor showers the Earth plays host to. They last for less time, and they are both more faint and less regular while they are happening.
The Quadrantid meteor shower is expected to peak on the night of January 3 and, weather permitting, will be visible until the early morning of January 4.
Nicola Maxey, a spokeswoman for the Met Office, said the weather “looks fairly cloudy for much of the country” on Friday night.
But Saturday will be mostly dry with variable cloud and some bright or sunny spells, particularly in the south, she added.
Meteor showers, or shooting stars, are caused when pieces of debris, known as meteorites, enter the planet’s atmosphere at speeds of around 43 miles per second, burning up and causing streaks of light.
Named after the now-defunct constellation of Quadrans Muralis, the Quadrantid meteor shower appears to radiate from near the constellation of Bootes beside the Big Dipper.
Unlike other meteor showers that tend to stay at their peak for about two days, the Quadrantid shower has a short peak period that lasts only a few hours.
Dhara Patel, an astronomer at the Royal Observatory Greenwich, told the PA news agency: “With up to 120 meteors per hour, the Quadrantids are considered one of the best annual meteor showers, however you’re likely to see far fewer meteors under imperfect viewing conditions.
“The peak of the shower only lasts a few hours compared to many other meteor showers which can stay at their peak for a couple of days, so there’s a limited opportunity to catch the peak.”
Unlike most meteor showers which originate from comets, it is believed the Quadrantids originate from an asteroid called 2003 EH1, which takes around five-and-a-half years to orbit the Sun.
While the meteors can be spotted all over the sky, Ms Patel advises facing towards the north-east, in the direction of the radiant, to catch as many of these shooting stars as possible.
She told PA: “Head out after midnight as the Moon sets below the western horizon so there’s less interference from moonlight.
“To give yourself the best chance of spotting the meteors, head out to an open and dark area, allowing your eyes time to become sensitive in the darkness by avoiding any bright sources of light like a mobile phone.
“Once you’re set up, be patient and enjoy the spectacle – it’ll be visible until dawn.”
Additional reporting by Press Association