The warning, which covers the majority of the east coast of the UK, is in place from midnight Saturday through to 6pm on Sunday.
Forecasters warn residents that the heavy rain due to lash the cityu copuld cause travel disruption and make journey times longer.
They also say that the flooding of businesses and and a few homes is 'likely'.
15-10mm of rain is expected in many areas during Sunday, with the potential for as much as 40-30mm in some places.
Breathtaking images of early morning lightning over Edinburgh show full scale of storm
What the Met Office experts say
Predictions indicate that most of Sunday will be wet for Edinburgh. Here is th eMet Office's tips and guidelines for what to expect:
- Spray and flooding on roads probably making journey times longer
- Bus and train services probably affected with journey times taking longer
- Flooding of a few homes and businesses is likely
- Some interruption to power supplies and other services likely
A spokesperson for the Met Office said: "Heavy rain is expected across parts of Scotland during Saturday night before extending to northern and eastern England during Sunday.
"Within the warning area many parts will see 15-30 mm of rain during Sunday with the potential for as much as 40-50 mm in places, much of this falling in a 6 hour period.
"At this stage, there is still some uncertainty regarding the location of where the heaviest rain will occur."