Alain Lesjongard, 55, who was on his way to an interview, suffered serious injuries when the District line train ran over him on 2 November.
His attacker, Alan Alencar, approached the city worker from behind and pushed him in the back with both hands just as the train pulled into the platform at Bayswater station.
The incident was captured on CCTV.
The driver hit the brakes but the train continued to travel three quarters of the way down the platform.
Mr Lesjongard managed to curl up into a ball and was able to crawl from underneath the carriage after the train passed over him.
He suffered a broken ankle and deep cuts to his neck and shoulders.
Alencar of Northcote Street, Edinburgh, walked away after the incident, the court heard.
On the day of the attack he had been on "temporary discharge from a facility where he was detained in Edinburgh", and had been visiting his mother who was also receiving psychiatric treatment.
The court heard that Alancar sent his "heartfelt apologies" to Mr Lesjongard and his family.
He will be sentenced on 9 March following psychiatric assessment.