Nadir Syed, 22, from Southall in west London, was arrested hours after buying a chef's knife in November 2014, days before Remembrance Sunday.
Woolwich Crown Court heard how he had been inspired by IS leaders urging attacks on Western targets, including police and soldiers.
The jury could not reach verdicts on two other men on trial.
Haseeb Hamayoon, 29, from Hayes, west London and Yousaf Syed, 20, from High Wycombe, Buckinghamshire, denied planning acts of terrorism. They will be retried.
The jury returned a majority verdict on Syed after more than 50 hours' deliberation.
The court heard how he had expressed admiration for the killers of soldier Lee Rigby and how he shared violent footage of beheadings from Syria and Iraq on social media.
Some of his conversations were made on encrypted applications, the jury was told.
The court heard that Syed had also tried to travel to Syria to fight with IS militants but had been stopped from leaving the country in January 2014.
In September 2014, IS militants issued a fatwa or decree calling on its followers in the West to carry out attacks at home, jurors were told.
In the weeks that followed, Syed's behaviour became increasingly worrying to MI5 and police intelligence officers who were watching him.
The court also heard how Syed had appeared in a video in which he stamped on a poppy and kicked it towards a drain, which prosecutor Max Hill QC said was demonstrative of his "attitude to the poppy as the remembrance image in this country".
By November last year he was actively searching for knives of "sufficient quality to source an attack", the court heard, and he was eventually arrested on 6 November shortly after buying a 30cm chef's knife.
Commander Richard Walton, head of the Metropolitan Police's Counter Terrorism Command, said: "This was an intense and lengthy operation by my officers, supported by the intelligence agencies, and I have no doubt that London is a safer place today with this conviction."
Syed will be sentenced at a later date.
A man has been convicted of preparing to carry out a knife attack in London, inspired by so-called Islamic State.