Friday will see the worst of the weather as the result of the storm, with up to 80mm of rain expected in some places.
Flooding is likely during heavy downpours brought by Storm Claudia, which was named by the Spanish meteorological service, the Met Office said.
The warning is in place from noon until the end of the day and covers parts of Wales, the Midlands, South West, South East and East of England.
The Met Office said: "Storm Claudia, previously named by the Spanish Meteorological Service, will bring rain that will become persistent and heavy during Friday.
"40-60 mm of rain is expected widely across this region with some places seeing around 80 mm; these higher accumulations more probable across the East Midlands, and higher ground in Wales and western England.
"Impacts may be exacerbated by strong easterly winds, as well as thunderstorms later Friday afternoon and evening."
These are the areas covered by the weather warning:
Offering advice to those affected by the weather warnings, the Met Office said: "Keep yourself and others safe; prepare to avoid travelling by road during potentially dangerous road conditions. If you must travel, ensure you watch for possible danger and drive cautiously.
"It is not safe to drive, walk or swim through floodwater, avoid it where possible and if you are affected by fast flowing or deep-water call 999, and wait for help.
"Preparing a flood kit could save you from loss or damage due to flooding to your home or business. In your flood kit have: insurance and any other important documents; a torch & spare batteries; a first aid kit, prescription medicines and supplies for looking after your family members or pets; and warm, waterproof clothes, blankets, food and water.
"Consider checking on vulnerable people that you know including older people, those with underlying conditions and those who live alone; they may need support with food and medical supplies.
"If you are worried about your health or that of somebody you know, ring NHS 111."