The man clambered on top of the bus in Elephant and Castle, in the south of the capital, sporting a head-mounted camera.
He then uploaded the shocking footage to his YouTube channel, where it has racked up more than 260,000 hits.
But Transport for London responded by condemning the “idiotic” bus-surfing stunt.
And the Metropolitan Police said officers were investigating the clip to see if any offences had been committed.
A spokesman for the force said: “Police are aware of the video and are looking into it.
“We urge people not to commit such an act as this, which is very dangerous and potentially life threatening.”
The thrill-seeker, known only as DyingLlama, claimed he had not broken the law.
Writing on YouTube, he said: “Technically, this isn’t ‘illegal’ because it’s only a civil matter here in the UK.”