The warning is in place from 6pm on Boxing Day to 9am on December 27, with heavy rain and high winds forecast.
A spokesman said: “Heavy rain combined with strong winds may lead to some disruption and flooding in places.
“There is a small chance that homes and businesses could be flooded, causing damage to some buildings
“There is a small chance of fast flowing or deep floodwater causing danger to life.
“Where flooding occurs, there is a slight chance of delays or cancellations to train and bus services.
“Spray and flooding could lead to difficult driving conditions and some road closures. There is a slight chance of power cuts and loss of other services to some homes and businesses
“There is a small chance that some communities become cut off by flooded roads.”
A spell of heavy rain will accompany strong southwesterly winds later on Saturday and early Sunday.
A statement added: “15-25 mm is likely to fall widely across this area with the potential for 40-60 mm over some hills. Recent wet weather and saturated ground makes this area more sensitive than usual to further heavy rainfall, especially across parts of southern Wales.
Locally, the regions affected are the East Midlands, Derbyshire, Yorkshire & Humber, North Yorkshire, South Yorkshire and West Yorkshire.
There could be snow flurries across higher ground, but these are not expected to cause disruption.