The video was taken by a concerned passenger on Wednesday at around 8am after the packed tram stopped at lights near George Street in Croydon and failed to move off again.
The shocked commuter said the driver was asleep for several minutes and people were forced to bang on the window to wake him up.
The video was taken on a Wimbledon-bound tram near East Croydon station, three stops from where a speeding tram derailed last November, killing seven passengers and injuring 51.
Tram operator FirstGroup has suspended the driver and launched an immediate investigation into the new footage, which TfL has passed to the Rail Accident Investigation Branch.
Mayor Sadiq Khan said he was "furious" about the latest incident, which follows reports of tram drivers asleep on the job and of speed limits continuing to be breached.
Last month, four current and former Croydon tram drivers admitted to the BBC that they had fallen asleep at the controls - and that a “dead man’s handle” safety device had failed to stop the vehicle.
Alfred Dorris, who was driving the tram that crashed on November 9, is thought by investigators to have “lost awareness” as he approached a bend at 46mph, three-and-a-half times the limit.
The latest video shows the driver slumped forward as passengers watch through his compartment window.
The commuter who took the video told the Standard around 50 people were on board at the time, including mothers with children. Most of them got off at the next stop because they were so concerned.
The man, who was on his way to work in Croydon, said: “The tram stopped at the lights because he just fell asleep. We had to hit the windows to wake him up.
“I think he was there for about two minutes. If we didn’t wake him up he’d have been asleep even longer.”