The Met Office has issued its highest level of warning as gusts of between 80 and 90mph are forecast to hit north east Scotland and north east England.
Police Scotland are warning people they should not attempt to travel in areas covered by a red warning, which lasts until 02:00 on Saturday.
A man has died after a tree fell on his car in Antrim, Northern Ireland.
Train operator LNER, which runs the East Coast Main Line between London and Scotland, said no services will operate north of Newcastle.
A Met Office amber warning for gales and a yellow alert for high winds and snow have also been issued for other parts of the country.
Train operator LNER has said there will be no services north of Newcastle as Storm Arwen hits the UK.
Image source, PA MediaThe firm runs the East Coast Main Line between London and Scotland.
Network Rail said it was closing the route north of Berwick-upon-Tweed from 17:00 GMT, and there could be further closures elsewhere on the route.
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Tonight's I'm a Celebrity...Get Me Out of Here! will be pre-recorded instead of the usually live show because of Storm Arwen.
The ITV programme is filmed at Gwrych Castle in north Wales, which is currently covered by a yellow warning of wind from the Met Office.
Image source, PA MediaAn ITV post said, external: "Tonight's I'm A Celebrity...Get Me Out Of Here! will be broadcast as a pre-recorded show rather than live due to the developing Storm Arwen and precautionary measures we're putting into place on production.
"Ant & Dec will record their links early evening and these will be played out during tonight's show.
"Our celebrities will remain inside the castle which is secure and we have contingencies in place to cover all weather scenarios to ensure the safety of our cast and crew."
Heavy snow has been forecast for some of Scotland's hills and mountains.
There is a yellow Met Office warning for snow for parts of the Highlands, Aberdeenshire, Perth and Kinross and Angus.
Forecasters said snow could accumulate to as much as 8cm (3in) above 300m (984ft) in upland areas, including at the Glenshee ski centre, near Ballater, where snow was seen on Friday afternoon.
Image source, Keith GeddesWind and snow at Glenshee ski centre near Ballater on Friday in a picture taken by Keith Geddes
The Mountain Weather Information Service has forecast "massive snowfall" for the Cairngorms overnight Friday and into Saturday, and the risk of wind-blown snow causing whiteout conditions.
Also, on Friday in the Cairngorms and south-eastern Highlands, the service warned of gusts of 100 to 120mph in hurricane-force winds.
Mountaineering Scotland, an organisation representing hillwalkers, skiers and climbers, has said it looked like "a good weekend for festive shopping or get cosy indoors".
The Met Office has issued the following shipping forecast for inshore waters between Berwick upon Tweed to Whitby at 16:30:
Strong Wind Warning in Force
Northwest six to gale eight veering north severe gale nine to violent storm 11, then decreasing seven or gale eight again later.
A 10-mile (16km) stretch of the A1 in East Lothian has been closed in both directions between Thistly Cross roundabout and Abbotsview Junction due to high winds.
Trunk roads company Bear Scotland said wind speeds of up to 84mph were forecast where there were bridges over the River Tyne near East Linton.
A diversion route is in place via the A199. This is expected to add approximately 10 minutes to affected journeys, says Bear Scotland.
Many people have been asking how Storm Arwen got its name.
BBC Weather presenter Jen Bartram said it was suggested by the public.
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BBC Scotland reporter Rachel Bell says there are increasingly treacherous conditions in Aberdeen.
"It is very windy here - the snow has been getting progressively heavier and there have been fallen trees across the region blocking roads," she says.
"We have seen videos from up and down the east coast of waves crashing over harbour walls and we've heard reports of very dangerous driving conditions due to debris on the roads."
The Met Office has several weather warnings, external in place covering large swathes of the north, eastern and western coastal parts of the UK.
Worst affected is the "red zone" along the eastern coast of Scotland and north-east England, taking in Aberdeen, passing close to Edinburgh, through the Scottish Borders, and down a strip along the coast of northern England past Newcastle and down to Hartlepool and Redcar.
The amber warnings for high winds - which cover likely travel disruption and damage - takes in a wider area over much of the eastern part of Scotland and north east England, including Dundee, Edinburgh, Newcastle and Durham.
There are yellow warnings for wind or snow covering all of Scotland, Northern Ireland, parts of northern England, much of Wales and parts of the south west of England. This is lower risk but suggests people should be alert for disruption.
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The north-east coast of Scotland is now feeling the force of Storm Arwen, according to BBC Scotland's Tyrone Smith.
He tweeted a video of trees down in Aberdeen this evening.
"Aberdeen is really getting battered by #StormArwen, external just now", he wrote just before 17:00.
"The power of the wind gusts is illustrated by this rush hour scene on Mid Stocket Road."
Network Rail is warning high winds of up to 100mph risk overhead power lines swaying and getting tangled on train equipment, causing damage and delays.
The network operator said strong winds could also blow debris and trees on to rail lines.
East coast route director Sarah Reid said staff were "doing all we can to keep services moving where possible and it is safe to do so".
Image source, GoogleMs Reid said the operator was "expecting major service changes tonight and into the weekend, particularly with the closure of the East Coast Main Line in and out of Scotland from 17:00".
Speed restrictions will mean longer journey times where trains are still running.
Passengers are urged to check before travelling with National Rail Enquiries or their train operator's website.
The Scottish Seabird Centre has shared footage of stormy conditions off the coast of East Lothian.
The visitor attraction in North Berwick is right next to the North Sea.
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Trees are being blown over and causing disruption as Storm Arwen sweeps across Scotland.
Trees are down in Aberdeen, and there is also a report of a tree blocking both lanes of the A96 south of Huntly in Aberdeenshire.
Police have already urged against travel in red warning areas.
Scotland's First Minister has urged people living in areas covered by the red warning not to travel.
In a tweet, Nicola Sturgeon said people in the affected area should heed the advice as the conditions posed a risk to life.
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Following a ministerial meeting of the Scottish government’s Resilience Room, deputy first minister John Swinney said travel should not be attempted "under any circumstances".
He said: “The decision by the Met Office to issue a rare red weather warning for strong winds signals a potentially damaging and dangerous risk to life in some areas of Scotland.
"The Scottish government is in close contact with local authorities and the emergency services to ensure people in the affected areas receive the latest information, advice and support where needed.”
Police Scotland has also urged people in the affected areas not to travel.
Photographer Simon Woodley captured these stunning shots of the stormy seas at Roker Pier in Sunderland shortly before the arrival of Storm Arwen on the coast of north-east England.
Image source, Simon Woodley
Image source, Simon WoodleyDue to the heavy winds brought by Storm Arwen, London North Eastern Railway has cancelled its 18:00 and 19:30 London Kings Cross to Edinburgh services.
All other services are also being heavily affected, with many terminating at Newcastle.
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BBC Scotland weather forecaster Joy Dunlop said red weather warnings were extremely rare and meant the conditions on the east coast would be "treacherous".
She said: "It is the highest warning so only issued if there is a genuine danger to life."
The worst of the conditions will be experienced tonight and the winds are forecast to ease after midnight, she said.
"By tomorrow morning these conditions will have eased a lot. So tonight if you can stay at home you should do so."
BBC Radio Newcastle will be broadcasting through the night running updates on the latest from Storm Arwen in the north-east of England.
They will be keeping an eye on all emergency services and hearing from people affected by the storm.
There will be up-to-date travel information as well. You can find BBC Newcastle here on BBC Sounds or on 95.4FM and DAB.
Some carriages have been removed from the Ferris wheel at Edinburgh's Christmas Market
The Christmas market in the centre of Edinburgh has closed due to high winds.
The city's Princes Street Gardens is hosting a market and various Christmas rides, which shut at 15:00.
Some of the carriages on the Ferris wheel were also removed as a precaution in the face of Storm Arwen.
A decision about the opening the market on Saturday will be made in the morning.
Storm Arwen disrupted travel and education across parts of Scotland on Friday.
More than a dozen schools were closed in the Highland Council area, and Wick High School - which was damaged by high winds - will remain closed on Monday.
All schools in Orkney were closed from lunchtime.
Ferry operator CalMac reported disruption to services across its west coast network, and Loganair flights to and from Shetland were affected.
There were wind warnings for trunk roads bridges, including the Skye and Tay bridges, and the A1 east of Edinburgh was closed to high sided vehicles.
Graeme Ogston
Tayside and Central Reporter
Image source, Dundee WinterfestThe organisers of Dundee WinterFest say the event will not open today as planned, due to the severe weather.
The event at Slessor Gardens features a big wheel, helter skelter and children's Christmas rides.
Organisers say it will now open tomorrow at 10:00.
Meanwhile, a Disney on Ice show in Aberdeen has been called off.
The P&J Live venue said the decision was taken following travel safety advice from Police Scotland.