The warning is in place from 2pm Thursday, March 1 until 8am Friday, March 2.
There is a potential of snow in the area which will become heavy as it spreads north, as well as “significant ice build up” and easterly winds overnight into Friday.
A Met Office spokesman said: “A weather system is expected to move slowly north through Thursday, intensifying and pushing north across the warning area from Thursday afternoon.
“As it comes into contact with the very cold air resident over the UK, it has potential to produce widespread snow, accompanied by strong to gale force winds.
“As less cold air follows from the south, there is a chance of snow turning to freezing rain bringing an additional significant ice risk.”
Surrey Search and Rescue have tweeted to confirm that the “team have been put on standby to support with the amber snow warning”.
Yellow weather warnings are also in place for Surrey and Hampshire until just before midnight on Saturday, March 3, as heavy snow and strong winds could potentially affect the area during Friday, followed by further bands of snow on Saturday.
Highways England issued a severe weather alert for roads earlier this week, urging drivers to be prepared before setting out on journeys.
Gritting teams were out treating roads to try and keep traffic moving, but head of road safety, Richard Leonard, said it’s “still important to drive to the conditions when snow is forecast”.
He said: “Drivers should plan their journeys, monitor weather reports and pack a snow kit of blankets, food, water and a shovel if they really need to travel.”
The South East Coast Ambulance Service (SECAmb) is also reminding people to take extra care and has created a winter checklist.
This includes wearing appropriate shoes, keeping your bedroom window closed on winter nights, wearing bright colours at night and heating your home to at least 18 degrees centigrade.