Heavy rain and gale force winds were expected across southern Scotland from lunchtime, with south-eastern areas expected to be hit worst.
The Met Office issued a "be prepared" amber alert for the Borders, Lothians and Fife.
The Forth Road Bridge was closed to double-decker buses and had speed restrictions.
Drivers were being urged to plan ahead today amid warnings of flooding and potential disruption on the roads.
The Glasgow area is expected to face gusts of up to 50mph and heavy rain tomorrow morning. However, high winds and rain are expected to ease by the afternoon.
Elsewhere, a woman was killed by a falling tree branch in London's Kew Gardens during rain and gusts of wind close to 30mph.
The woman, believed to be around 30-years-old, was pronounced dead at the scene yesterday afternoon.
Wind speeds in the area reached a peak of 30mph at 4pm yesterday and were likely to be close to that at the time of the woman's death.
The Environment Agency has issued 56 flood alerts: 31 in the south-west of England, 19 in England's north-east and six in the Midlands.
Marc Becker, from the Scottish Environment Protection Agency, said: "Today it will be wet across most of eastern and southern Scotland, including the central belt, with the heaviest rain expected in the east of Scotland from the Borders up to parts of Angus.
"We are working closely with the Met Office to get a better picture of the potential flooding impacts as a result of this heavy rain."
The Scottish Government's Transport Minister Keith Brown said: "In light of the Met Office warning for wind and rain in many parts of the country, our trunk road operating companies have all their resources available, including patrols, and will pre-position resources in areas of special attention.
"The Traffic Scotland website, variable message signs and traffic internet radio are being used to provide up-to-date information to the travelling public, allowing them to plan and amend their trips accordingly."