The forecast of heavy rain follows on from warnings over severe gale force winds which begin on Tuesday afternoon.
The wind warning covers Tuesday from 15:00 and all day Wednesday.
Rain will be heavy and persistent for much of Wednesday with some large rainfall totals building up, particularly over south-facing hills.
The amber warning was issued for Strathclyde; Central, Tayside and Fife; and Dumfries, Galloway, Lothian and Borders.
The Met Office said: "A waving cold front is expected to become slow moving over western Britain during Tuesday night and for much of Wednesday, associated with a strong, moist southwesterly airflow."
It forecast rainfall accumulations of 2cm to 4cm, with 8cm over some higher ground.
It said some exposed locations in southwest Scotland could expect 10cm to 15cm (4in to 6in) of rain.
Gusts of 50-60 mph are expected to affect many parts, and 70mph in some exposed locations.
Jim Fraser, Scottish Borders Council's emergency planning officer, said: "The risk is very much dependent on the level of rainfall and where it falls, and at this stage there is still a degree of uncertainty in respect of these details, and also the timing of the rainfall.
"However, I would urge all Borderers to be vigilant and keep an eye on the Met Office and Sepa websites for updates on the weather and flood warnings.
"People should be preparing for the impact of this forecasted heavy rain as early as possible, which will help to mitigate the impacts when it actually arrives."
The Met Office has issued an amber "be prepared" weather warning for heavy rain across central and southern Scotland on Wednesday.