The Northwest of Scotland is set bear the brunt of the storm, with the Met Office issuing an Amber weather warning for this region.
Although most of England is set to be spared the worst, South Yorkshire and the North Midlands will still see strong gusts and some heavy rain.
Storm Abigail is set to be followed my much colder conditions than of late with snow forecast for the hills and mountains of North Wales northwards.
Abigail is the first storm to be officially named by the Met Office.
Earlier in 2015, the Met Office asked the general public for suggestions for names for storms.
The full list of names chosen for future selection are: Abigail, Barney, Clodagh, Desmond, Eva, Frank, Gertrude, Henry, Imogen, Jake, Katie, Lawrence, Mary, Nigel, Orla, Phil, Rhonda, Steve, Tegan, Vernon and Wendy.
A storm will be named when it is deemed able to potentially cause "substantial" impact on the UK or Ireland.
They will be taken from the list, in alphabetical order, alternating between male and female names. This is the same naming convention as that used for tropical cyclones in the US.