The warning covers Edinburgh and the Lothians and was issued on Friday morning by the Scottish Environment Protection Agency (SEPA).
It has been reinforced today with the message that people should take care while out and about.
The agency said that heavy rain would fall overnight and continue into Saturday morning, a statement said: “There is a risk of localised flooding of low lying land and roads from smaller watercourses and surface water.
"At this stage the greatest risk is in the East of the area."
The Met Office has predicted that the weather will start to brighten up as Saturday goes on, with sunny spells potentially breaking through in the late afternoon.
Elsewhere in Scotland will see a drier and slightly brighter day.
The Highlands, particularly around Inverness and across Caithness and Sutherland, are forecast to be overcast for much of the morning, but sunny spells will increase through the afternoon, with a maximum temperature of 16C.
Similarly, across Glasgow and Lanarkshire Saturday began overcast with heavy cloud, however, it is predicted to stay dry for most of the day.
Temperatures will reach a high of 18C with light winds.
Grampian will see a little bit more rain, with drizzles forecast throughout the morning.
As the afternoon rolls in there is potential for some sunshine to cut through the clouds.
Temperatures won’t reach above 15C though with northerly winds persisting for most of the day.