The warning is in place from 9am until 11.59pm today.
Frank Saunders, a chief meteorologist at the Met Office, said: “Strong winds arriving across the west through Tuesday morning, will spread inland and reach eastern areas through the afternoon and early evening.
"Gusts of 45-50mph are expected widely, with 60-70 mph in exposed coastal locations.
“The strongest winds will ease across inland areas into the overnight period.”
Barra is the second major storm to hit the country in the last fortnight following Storm Arwen which left thousands of people in the north of England and Scotland without power – and some are still yet to be reconnected.
The storm is will initially batter the Republic of Ireland before continuing west towards the UK.
As well as the wind, there are also warnings for potential snow on higher ground as the storm brings rain in with the wind.
Brent Walker, deputy chief meteorologist, said: “A band of rain will turn to snow across northern England and Scotland through Tuesday.
"Two to five centimetres of snow is expected to accumulate quite widely across the warning area, but locally this could reach10 centimetres, particularly in parts of the Southern Uplands and Highlands.
“Strong south-easterly winds will also lead to snow drifting in places, particularly over the highest routes, adding to poor visibilities.”