Footage of the unnamed man was reportedly filmed in April by a passenger but only published by The Sun after the Croydon tram crash on 9 November.
A spokesman for rail company First Group said: "The driver involved in the video has been removed from duty pending the outcome of the investigation.
"He will now be subject to a full investigation so it would not be appropriate to comment further at this stage."
The passenger who recorded the footage told the newspaper: “It was the most surreal thing because the tram is zooming along and the driver seems to be falling asleep.”
"He reminded me of someone who dozes off in a meeting - except if you doze off in a meeting you are not killing anyone."
After the footage was released, Mayor of London Sadiq Khan said: “I am extremely concerned by this video. People will understandably be very worried.
"It is important that First Group, who operate the trams, and Transport for London urgently and fully investigate this.
"I will make sure any necessary action is taken, and that all steps are taken to make sure these trams are as safe as possible.”
FirstGroup said they were not aware of the video before it was published.
Crystal Palace and Manchester City fans fell silent before kick off at Selhurst Park today as they paid tribute to the victims of the crash.
Both sides and their supporters observed a minute's silence in honour of the six men and one woman who were killed in the tragedy.
Two of the victims - named as 19-year-old Dane Chinnery and Philip Seary, 57, were fans of the Eagles.
In a statement on its website, Crystal Palace said: "Many members of the Croydon and wider community have been affected by this accident and as a club we stand together with the community at this very difficult time."
After the tribute the club tweeted: "Impeccably observed minute's silence by both sets of fans and players in memory of the victims of the Croydon tram crash."
The others killed were Philip Logan, 52, Dorota Rynkiewicz, 35, and Robert Huxley, 63, all from New Addington, and Mark Smith, 35, and Donald Collett, 62, both from Croydon.
Additional reporting by agencies
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