The station will be running a limited service this evening after closing this morning, operator Network Rail said.
All services had been cancelled for much of today after wind speeds reached 102mph.
Flights to and from Edinburgh Airport - which had been closed due to high winds and damage to the terminal building - recommenced as of 2pm.
BAA said 62 flights were cancelled as a result of the weather.
Matt Dobson, a forecaster with Meteogroup, said the winds peaked in the central belt this morning and moved to the north of the country in the afternoon.
More gales are expected tomorrow but wind speeds are likely to peak at 40-50mph, the Met Office said
If you have pictures of the impact of the storm in your area email [email protected] or phone the newsdesk on 0131 620 8734