Peebles, Jedburgh, Greenlaw and Shiplaw in the Borders and Haddington in East Lothian have been put on alert, with rivers expected to rise and potentially cause localised flooding.
It comes at the end of Storm Angus, which brought flooding and major disruption to parts of England and Wales.
One woman died off Folkestone harbour in Kent, while searches are continuing for a missing pensioner in South Wales thought to have been caught up in the weather.
Almost 150 ferry passengers travelling from the Republic of Ireland to Wales were forced to spend Monday night at sea due to the conditions.
The wet weather is expected to be short-lived in Scotland but is likely to then be replaced by freezing temperatures.
Met Office meteorologist Alex Deakin said: “An area of low pressure is still across the UK and feeding in showery rain across eastern Scotland which will slowly peter out.
“Overnight the low pressure moves away taking the showers with it, leaving clearer skies, however that brings frost with another cold night in store across Scotland and Northern Ireland.
“In rural areas we could get down to negative double-digits.”
Police are warning people in the flood risk areas to be aware of changing conditions.
Chief Inspector Matthew Paden, local area commander for East Lothian, said: “This flood warning is a precautionary measure and we are advising to take appropriate action to mitigate any flooding.
“For the most up to date information, get in touch with Floodline immediately and avoid contact with flood water.”