Matthew Connell posted a short clip on X, formerly Twitter, which captured the hairy moment the plane appeared to wobble as it came in to land on Sunday night.
He told how the flight from Ibiza to London City Airport was diverted to Gatwick due to the storm, which left the entire UK under a yellow weather warning until midday on Monday.
"I’ve had my fair share of flights but this was one of the most unstable approaches I’ve expected," he wrote.
"Fun but violent. You can hear the relief from the cabin."
His video clip captured relieved passengers clapping, cheering and whistling as the plane finally touched down, with one passenger shouting: "Go on, geezer".
Gatwick Airport confirmed it accepted five diversions from other UK airports on Sunday, due to weather.
Another clip posted on X on Sunday captured passengers on a Jet2 flight from Alicante clapping, as the plane landed in windy conditions at Edinburgh.
The passenger posting the clip wrote: "Well done to Captain David Livingston and crew on the Jet2 LS776 ALI-EDI getting us all home safely through #StormIsha landing in 110mph winds was not a good experience but we were clearly in safe hands!"
One TUI flight travelling from Sharm el Sheikh to Glasgow Airport declared an emergency due to Storm Isha, and was diverted to Manchester Airport.
The Met Office said the highest recorded wind speed during Storm Isha was 99mph at Brizlee Wood in Northumberland, with gusts of 90mph at Capel Curig in Snowdonia on Sunday.
High winds were expected to continue on Monday morning, with a yellow weather warning in place across the UK until midday, and commuters hit by widespread travel disruption.
Air traffic control restrictions were in place, leading to flight cancellations and causing some planes to divert.
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Heathrow Airport's departures board indicated several flights were cancelled on Monday, to destinations including Edinburgh, Amsterdam, Rotterdam, and the Isle of Man.
A British Airways spokesperson said: "Like other airlines, we have had to make schedule adjustments due to the adverse weather conditions across the UK and Europe caused by Storm Isha.
"We've apologised to our customers for the disruption to their travel plans and our teams are working hard to get them on their way as quickly as possible."
National Air Traffic Services said: “Due to adverse weather conditions across the UK, temporary air traffic restrictions are in place. Restrictions of this sort are only ever applied to maintain safety.
“Our teams are working closely with airports and airlines to minimise disruption. Passengers should check the status of their flight with their airline.”
Scotland has been hit particularly badly by the storm.
A red warning for wind in north-east Scotland was in place until 5am on Monday, with amber warnings covering much of the UK until 6am and further yellow warnings covering the entire country until noon.
A further yellow warning for wind for Scotland, Northern Ireland, north Wales and northern England is active from 4pm on Tuesday until noon on Wednesday.
No train services were running across all of Scotland on Monday morning.
Network Rail said it expects train services in Scotland to remain suspended until around noon after what it described as “a wild night".
