Many have headed for Praia do Norte in Nazare, Portugal, where Hawaiian surfer Garrett McNamara set a world record for the largest wave surfed in 2011.
The storm created huge swells in the sea off Scotland leading to warnings from the Coastguard and RNLI.
The swell off Nazare has been recorded at a maximum of height of 40ft (12m).
But South Devon-based website Magicseaweed.com, which provides surfers with swell charts and surf forecasts, said the swell grew in size as it neared the beach.
Three years ago, Mr McNamara caught a 78ft (23m) wave to beat the previous 2008 record by more than a foot.
The Atlantic storm hit Scotland late on Tuesday and during Wednesday. The Western Isles, Orkney and Shetland and parts of the north and west mainland coast were the worst affected.
Wave heights measured west of South Uist by the University of the Highlands and Islands peaked at about 49ft (15m) on Wednesday.
The storm started in the Arctic where it had rapidly developed in strength in a process known as explosive cyclogenesis, or what some scientists and forecasters refer to as a "weather bomb".
Pressure at the centre of the storm dropped quickly in the space of 24 hours as it passed by the south of Greenland on a strong jet stream running in excess of 230mph.
As well as Nazare, surfers have been in Bilbao, northern Spain, for a Punta Galea Big Wave World Tour surfing event. It has also benefitted from swells created by the storm.

A woman got out of the vehicle and an unknown man jumped in and took the car.
Police said it happened at Boucher Crescent in south Belfast at about 17:25 GMT.
Members of the public managed to stop the car but the man fled on foot.
A short time later a man in his 30s was arrested and remains in custody. The two children were unharmed.

In total, 99 were seized by police under the Dangerous Dogs Act, down 60 from 159 in 2015.
Figures were obtained from all Welsh police forces using a request under the Freedom of Information (FOI) Act.
National Police Chiefs' Council spokesman Deputy Chief Constable Gareth Pritchard said many people bought dogs without knowing their temperament.
North Wales Police said attacks rose from 158 to 246 in the area. In south Wales, it went up from 298 to 332 and in Dyfed-Powys' area the numbers increased from 45 to 53.
Gwent Police recorded number decreased from nine to three, in the figures obtained for BBC Radio Wales' Jason Mohammad Show.
Dep Ch Con Pritchard, who also works for North Wales Police, said: "We are concerned people are buying them on the internet.
"They are buying at car boot sales and buying at motorway service stations.
"They are not seeing the dog in its environment and understanding its temperament."
He added that if people are thinking of buying, they should "see the dog with the mother, see the temperament and understand the power and the attributes of the dog".
Despite the increase in attacks, the same FOI figures show the numbers of seizures under the Dangerous Dogs Act have fallen from 159 to 99.
In North Wales Police's area, the figure went down from 32 to 16, in south Wales, from 113 to 72, there were two seized in 2015 and 2016 in Gwent and in Dyfed-Powys, the figure dropped from 12 to nine.
Jayne Dendle, from Swansea, is a member of the campaign group Born Innocent, that lobbies against the Dangerous Dogs Act.
"Owners can just go out and buy any puppy, everything is totally unregulated and people don't necessarily see a dog as a lifetime pet and don't put the effort and energy they need into it," she said.
"Socialising it and exercising it. A dog is a big commitment and we need to put a great deal of time into that."
Some of the world's top surfers have been riding massive waves generated by the Atlantic storm that hit Scotland.
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A man has been arrested after a car was stolen with two young children inside.
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There were 634 reported dog attacks in Wales in 2016, up by 124 from the year before, according to latest figures.