Exposed coastal areas could see winds as strong as 95mph, while inland areas are forecast to experience 80mph winds.
People can expect some travel delays both on the roads and the railways and there is a possibility of some power cuts across the country.
Meteorologists anticipate up to 20cm of snow could accumulate over high ground, with up to 5cm possible in some lower areas.
The Met Office warned that blizzard conditions can be expected alongside the snowfall, due to the winds being so high.
Overnight from Thursday into Friday it is expected to be dry but cloudy in Edinburgh with sleet forecast to start falling at around 6am.
This will continue throughout the morning and will turn to heavy snow at around midday.
The rest of the day is expected to be cold and windy with widespread sleet continuing.
Throughout the afternoon it is forecast to gradually turn drier but strong northeasterly winds are expected with a maximum temperature of just 2 C.
"Storm Eunice is expected to track eastwards from early on Friday, bringing the most significant winds to the central and southern areas of the UK, with some gusts possible in excess of 95mph in exposed coastal areas," said Met Office Chief Meteorologist Frank Saunders.
Looking towards the weekend the Met Office has predicted Saturday will be mainly dry and bright with light winds, while Sunday will start off wet and clear and turn to just a few blustery showers. At the moment Monday is forecast to be windy by dry.
Storm Dudley resulted in travel chaos with ScotRail announcing that almost all services would be stopping at 4pm on Wednesday as a precaution. Most reopened on Thursday morning but the operator is continuing to monitor Storm Eunice to decide whether further services have to be suspended.