Witnesses said the driver then sped off through a red light.
A white van driver knocked over a cyclist on Bristo Place minutes after he had reportedly hit a pedestrian on Princes Street.
Video footage shows the moment the driver speeds off and through a red light in front of Bedlam Theatre after a cyclist confronts him about his driving.
With seemingly no care for the cyclist's safety, the van driver drove off while shouting and swearing, dragging the cyclist along with him and causing him to fall off.
Eyewitnesses said the victim's leg also went underneath the van during the incident which took place at around 4.45pm on Wednesday October 30.
The man who took the video footage, who cannot be named, said the driver sent the cyclist "flying".
He said: "I heard a van revving up and lots of shouting at the crossing on the Mound and put on my helmet camera in time for this guy in the van to send the lad on the film flying. He hurt his back and I think one leg went under the van.
"Lots of people witnessed it and it turned out the the same guy had just a few minutes earlier hit a pedestrian on Princes Street. He then hit a cyclist with his mirror swerving round him trying to get away.
"Drivers were following him and a delivery boy on his bike had given chase. The van couldn't move because of the red light and the boy was photographing his registration number while the driver was shouting and swearing at him. He then moved the van and basically flattened the guy. He must have panicked as the police were racing up towards him."
"He even had a woman and a wee Jack Russell on the front seats, and a disabled blue badge so it is a distinctive vehicle.
"I gave police a statement and hope they catch the guy. He was a nut. Really dangerouns and desperate."
A spokesman for Police Scotland said: "Police Scotland can confirm that a call relating to a road crash between a cyclist and a van in Forrest Road in Edinburgh was received at 4.45pm on Wednesday 30 October 2019.
"The male caller did not leave any details and police have not been able to trace or speak to him yet. Police Scotland is also aware of footage posted on line which relates to a crash between a cyclist and van, which may have taken place in Bristo Place in Edinburgh, a road which runs off Forrest Road.
Inspector Keith Mailer at Howdenhall Police Station said: " Inquiries to identify those involved and the circumstances surrounding this incident is underway.
"I would ask anyone who can assist with further details, including the cyclist and the van driver, to call Police Scotland on the 101 number, quoting reference number 2531 30 October 2019."