Sir Robert Malpas went “flying” from the platform at Marble Arch Station when he was shoved by Paul Crossley.
The 91-year-old industrialist was rescued by a bystander but suffered a fractured pelvis and a head wound.
An Old Bailey jury found Crossley, 46, of Leyton, east London, guilty of two counts of attempted murder.
The second related to an unsuccessful attempt to push another passenger, Tobias French, on to the tracks at Tottenham Court Road station earlier on 27 April.
Sir Robert watched proceedings from the public gallery and could be seen sobbing after the jury left, BBC Journalist Jeremy Britton reported from court.
‘One minute to next train’
CCTV footage of the attack drew gasps from the court’s public gallery when it was played in court for the first time.
In it, Sir Robert can be seen walking along the platform, wearing a brown Burberry raincoat, suit and tie, and carrying an umbrella.
He is then approached from behind by Crossley, who sends him sprawling on to the tracks with a two-handed push.
In a statement read in court, Sir Robert, who was knighted by the Queen in 1998, said: “I felt myself flying over the tracks and landing on the rails.”
He was rescued by passer-by Riyad El Hussani, who leapt from the platform to save him with one minute until the next train.
Prosecutor Benjamin Aina QC said: “Mr El Hussani bravely left where he was stood and ran down the platform and then jumped down on to the tracks.”
“As he landed he threw his hand forward to stop himself falling and he briefly touched the electrified track, causing a burn to his right hand.”
The court heard members of the public pulled Sir Robert back on to the platform after Mr El Hussani managed to get him to the edge.
Mr French, the court heard, managed to keep his balance when he was earlier pushed by Crossley as a train pulled in to Tottenham Court Road station.
The defendant told the court he meant “to scare” Mr French, who had “looked at me a bit funny”.
Crossley told jurors his victims were chosen at random but claimed he had not intended to kill them.
He had taken crack cocaine the previous day, the court heard, and began feeling paranoid as he made his way to the West End to get coffee.
‘Brave actions of public’
He said he was having a panic attack at the time he attacked Sir Robert, intending to “push him over on to the floor”.
Crossley had previously admitted the lesser charge of attempting to wound with intent against Sir Robert.
He had denied an alternative count of attempting to cause grievous bodily harm to Mr French.
Crossley, who was diagnosed with paranoid schizophrenia when he was 17 years old, will be sentenced on 9 November after a psychiatric report has been prepared.
Det Insp Darren Gough, of the British Transport Police, said: “We could have easily been dealing with a double murder investigation had it not been for the brave actions of the public who stepped in and restrained Mr Crossley, and assisted the victims.
“I would like to remind the public that this type of incident is very rare and millions of journeys are made across the Underground without incident.”