Storm Éowyn was “probably the strongest storm” to hit the UK in at least 10 years, the Met Office has said.
Parts of Ireland had the highest windspeeds since records began after they reached 114mph in Mace Head, County Galway, on Friday.
Kacper Dudek, 20, died after a tree fell on his car at Feddyglass, Raphoe in County Donegal, early on Friday. Irish police are investigating the incident.
Nearly a million properties were without power across the island of Ireland after Storm Éowyn swept in strong gusts that damaged buildings and blocked roads.
Further wind and rainfall is forecast. Some areas could get up to 80mm of rainfall while 10mm to 20mm should fall quite widely and 30 to 50mm could fall over high ground. The Met Office has issued several amber and yellow weather warnings over Saturday and Sunday.
A yellow warning for strong winds is in place for much of Scotland until 3pm on Saturday, where gusts could reach 50-60mph inland, 60-70mph on exposed coasts and hills and possibly 70-80mph in the Northern Isles.
The meteorologist Tom Morgan said: “The winds have still been strong nonetheless overnight, so it’s definitely not the calm after the storm today.
“It’s certainly a calmer day, but there are still going to be strong winds around, particularly across Scotland today, but for most of the UK, it’s certainly a much brighter and less windy picture, at least for most of Saturday.”
On Saturday morning, Network Rail Scotland said nearly 400 “incidents of damage” had been found including more than 120 reports of fallen trees.
Signalling systems, overhead wires, stations, boundary fencing, level crossings and train depots were also damaged, it added.
NIE Networks said at 11am on Saturday about 185,000 properties remained without power in Northern Ireland.
Derek Hynes, the managing director of NIE Networks, said it was believed there were more than 4,000 locations where the network has been damaged by the wind or fallen trees.
“Right now, we are prioritising faults which affect the largest numbers of homes and businesses. It is likely that it will take us up to 10 days to get to the final locations and restore power to those residents,” Hynes said.
On Friday, the PSNI assistant chief constable, Davy Beck, said it would take days to assess the full impact of the “severe” storm.
“We’re only now starting to see the number of calls start to rise in respect of impacts, concerns for safety, and indeed, more and more reports in respect of roads blocked and issues as a consequence of that,” he said.
“So, I think it’s going to be a number of days before we can fully understand the full impacts of this storm but certainly this was a severe storm.”
The utility company Uisce Éireann said about 138,000 people had no water as of Friday evening, and a further 750,000 people’s supplies were at risk.
More than 1,100 flights were cancelled on Friday, with Dublin, Edinburgh, Heathrow and Glasgow airports the worst affected.
On Sunday, a yellow wind warning covering south-west England, English and Scottish coasts around the Irish Sea, Wales and Northern Ireland will be in place from 8am to 3pm, with 50 to 60mph gusts expected widely in the warning area.
A yellow rain warning covering southern and central England and Wales will also be in place from 8am on Sunday to 6am on Monday.