After a dry start on Monday, the gales are forecast to push across Britain as the day progresses.
A Met Office spokesperson said: "Gusts of 40 to 50mph are expected quite widely inland, with exposed coasts and hills having gusts of around 60 miles per hour, perhaps locally 70mph".
The warning will be place from 7am until midnight on Monday.
Status Orange Weather Warnings are in force for all counties with a Status Red in marine areas.
"The high winds will create very rough sea conditions, the public are advised to AVOID ALL coastal areas including beach fronts, sea walls, promenades and sea ports as there is risk of coastal flooding and damage due to over topping waves leading to risk of injury & danger to life".
She said the second corps of strong winds would impact in the afternoon mainly affecting parts of the west and northwest.
There is the potential for power cuts and other services to be affected.
According to the warning: "An area of very strong winds will move eastwards across the United Kingdom through Monday afternoon and evening, clearing eastwards overnight".
On its website, the meteorological service warns: 'The strongest winds are expected around exposed coasts and hills.
Strong winds and heavy rain battered parts of Scotland on Saturday, causing road closures and rail disruption as gritters attempted to deal with icy conditions.
This warning is for Central, Tayside and Fife, Grampian, Highlands and Eilean Siar, London and South East England, North West England, Northern Ireland, Orkney and Shetland, SW Scotland, Lothian Borders, South West England, Strathclyde and Wales.
The yellow wind warning covers Dublin, Carlow, Kildare, Kilkenny, Laois, Longford, Louth, Wicklow, Offaly, Westmeath, Meath, Cavan, Monaghan, Roscommon and Tipperary.
'Here gusts of 60-70 miles per hour are likely, with a few sites perhaps seeing gusts to 80 miles per hour.
Ms Dillon said the winds would only gradually ease on Monday with and another band of unsettled weather would follow on Tuesday bring sleet and even snow to higher ground.