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During the trial, the court heard Junead Khan had been identified under the government's anti-extremism programme - and had mocked it after police visited him in 2014.
He sent a message to his 23-year-old uncle, Shazib, also from Luton, saying he was laughing out loud because police left a card asking him to call them.
He later met with officers and afterwards sent a message saying: "Hopefully the last I hear from them."
Commenting after the verdicts, police said Junead Khan "repeatedly rejected police offers to help divert him from radicalism".
Officers working as part of Prevent - the government's drive to stop people becoming terrorists or supporting terrorism - visited him four times in 2014, the Metropolitan Police said.
But he refused help and became "more embroiled in extremism", and after his arrest police found material including "bomb making guides and terrorist propaganda".
Commander Dean Haydon, of the Metropolitan Police's Counter Terrorism Command, said Junead Khan had done extensive research on how to make a bomb.
Police also recovered British and US flags stolen from a diner in Dunstable. These were "potentially to be used for a symbolic act during the terrorist attack", the Met said.
In July 2015, Junead Khan had an encrypted online conversation with Junaid Hussain, a British IS operative in Syria.
He was sent instructions on how to build a bomb and was told to use it against police if they arrived on the scene of his planned attack.
Days after this online conversation he carried out internet research into buying a large knife - but was then arrested at his workplace.
The following month Junaid Hussain was killed in a US missile strike - one of only a few British IS operatives who have been targeted in this way.
Hussain was a hacker and IS propagandist, and US military spokesman Colonel Steve Warren said he had the potential to "radicalise and inspire violence in foreign countries around the world".
Sue Hemming, head of the counter terrorism division of the Crown Prosecution Service, said: "Through early detection and prosecution of these individuals more serious crimes have been avoided which could have had devastating consequences in the UK or Syria."
The verdicts came after a six-week trial at Kingston Crown Court.
The men were remanded in custody and will be sentenced on 13 May.