Firefighters eventually removed the protester, James Brown, from the British Airways aircraft and he was arrested.
He live-streamed his actions on Facebook.
“Okay, here I am, top of a f****** aeroplane at City Airport… I managed to get on the roof,” he said.
“Oh man I’m shaking… This is all about the climate and ecological crisis. We’re protesting at government inaction on climate and ecological breakdown. They declare a climate emergency and do nothing about it.”
He said it was “scary” because he “hates heights”.
Mr Brown, who is partially sighted, won a bronze at the London Paralympics in cycling but was later banned for a doping violation.
Last month, he was arrested for trying to fly a drone at Heathrow.
Met Commissioner Dame Cressida Dick described his actions as “reckless, stupid and dangerous”.
Hundreds of people attempted to shut down the airport in protest at the impact of air travel – part of the global Extinction Rebellion demonstrations.
Protesters say airport expansion plans are incompatible with the government’s commitment to cut emissions to net-zero by 2050.
Activists are beginning what they call a three-day “Hong Kong-style occupation of the terminal building” and say they want to stop flights by lying, sitting or gluing themselves in front of departure and arrival gates.
In a separate incident, a plane returned to the terminal after another protester disrupted the flight, according to Sky sources.
Footage shared by a Twitter user showed a protester refusing to take his seat on a Dublin-bound flight.
He can be heard telling an air hostess: “I don’t wish to travel with you but I don’t wish to get off.”
He adds: “I’m extremely sorry for the inconvenience.”
A passenger is then heard saying to the cabin crew: “Can you do us all a favour and remove him from the plane?”
The protester continues: “We have two generations of human civilisation left if we carry on doing what we’re doing.”
Extinction Rebellion said it intended to “peacefully occupy and shut down” the airport’s terminal building.
Sky’s home affairs correspondent Mark White said a protester also managed to get onto a low roof in the terminal building.
Outside the airport, protesters blocked traffic near the drop-off zone, while police also dealt with demonstrators who occupied the Docklands Light Railway station, gluing themselves to the entrance.
Extinction Rebellion spokesperson Rupert Read said: “By non-violently shutting down this airport, in homage to the style of the Hong Kong democracy protesters, we are demonstrating the utter frailty of the transport systems that countries such as ours, unwisely, have come to depend upon.”
The group said hundreds had signed up to take part and that they were willing to risk being arrested.
Metropolitan Police deputy assistant commissioner Laurence Taylor said there were plans to intervene and “deal proactively” with anyone trying to disrupt the airport.
London City Airport CEO Robert Sinclair said only two flights had been cancelled, and the airport had “remained fully operational throughout the day”.
He added: “If you are flying from London City Airport this evening or tomorrow, please do check the status of your flight with your airline before travelling to the airport.”
The sit-in comes on the fourth day of the Extinction Rebellion climate protests, which are taking place across central London and other cities worldwide.
Hundreds of officers are being drafted in from across England and Wales to help the Met with the demonstrations.
More than 1,000 people have been arrested.