Face of Nation : Paul Crossley shoved 91-year-old Sir Robert Malpas at Marble Arch in April 2018, after earlier trying to push Tobias French at Tottenham Court Road.
Crossley, 47, of Leyton, east London, was found guilty of two counts of attempted murder and will serve a minimum of 12 years.
A judge described him as a “grave and enduring risk to the public”.
Judge Nicholas Hilliard QC told the Old Bailey that Crossley had carried out two attacks in “terrifying circumstances”.
The court previously heard Crossley, who has paranoid schizophrenia, had not taken his medication on the day of the attacks and had used £600 worth of crack cocaine the day before.
In the first of the attacks on 27 April, Crossley tried to push Mr French on to the tracks as a train entered the station, but the professional sportsman managed to keep his balance.
During the trial, Crossley said he had meant “to scare” Mr French, who had “looked at me a bit funny”.
Judge Hilliard said CCTV footage of the attack had been “terrifying to watch” and Crossley fled, before picking out Sir Robert due to his age.
Crossley “consciously and deliberately sought out a more vulnerable victim”, according to the judge.
He added: “The moment you saw Sir Robert you went for him.”
After being pushed on to the tracks, Sir Robert was rescued by Riyad El Hussani, who jumped down from the platform and pulled him away from danger.
Judge Hilliard said teacher Mr El Hussani acted with “great bravery and no regard at all for his safety”.
Former industrialist Sir Robert, who was knighted in 1998, spent more than a week in hospital with a fractured pelvis and a head wound.
The “driving force” for the attacks was “drug abuse and its consequences” rather than paranoid schizophrenia, the judge added.
Crossley will first be sent to hospital until his health improves and then to prison to serve the remainder of his sentence.
