Fourteen notices were issued by the Scottish Environment Protection Agency (Sepa) for Wednesday, mostly covering Dumfries and Galloway.
Warnings have also been issued for Grangemouth, Culross, Longannet and Kincardine in the central and Fife areas.
The fifth storm of the season has moved into the North Sea but Met Office warnings for high winds remain in place until Wednesday evening.
Storm Eleanor lashed other parts of the UK with violent storm-force winds of up to 100mph, leaving thousands of homes without power and hitting transport links.
Several major bridges south of the border were closed due to high winds and there were numerous reports of fallen trees blocking roads including the M25.
In Scotland, the Met Office issued an amber “be prepared” warning of wind for the southernmost fringes of the country overnight, which has now expired.
However, yellow “be aware” warnings of high winds remain in force for south-west Scotland, Lothian and Borders and the very southern reaches of Strathclyde. They are valid until 6pm on Wednesday.
A 77mph gust was recorded at West Freugh and 72mph at Dundrennan, both in Dumfries and Galloway, on Tuesday evening, according to the Met Office.
The strongest winds in that area are thought to have passed.
Issuing its flood alert for Dumfries and Galloway, Sepa said high tides combined with a large storm surge are expected throughout the region and warned that coastal communities and roads may experience flooding around high tide on Wednesday.
The agency has also issued flood alerts for coastlines in northern Scotland.
Police said they had received some calls overnight about trees blocking roads in the south west of the country but there were not thought to be any reports of injuries.
Drivers in some areas have been advised to use caution due to water on road surfaces.
The latest warnings come days after the country was hit by Storm Dylan.