Kazi Islam was said to have used "flattery and threats" in exchanges on social media to try to persuade Harry Thomas to kill two soldiers and buy ingredients for a pipe bomb.
Islam, 18, of Newham, east London, was found guilty at the Old Bailey of preparing to commit acts of terrorism.
He claimed he was conducting research.
Islam was convicted by a majority of 10 to two and will be sentenced on 29 May.
He was remanded in custody and told by Judge Richard Marks that a custodial sentence was inevitable.
The trial was told Islam befriended the then 19-year-old Mr Thomas in October 2013 - five months after Fusilier Rigby was attacked in the street near Woolwich Barracks - after meeting him the previous year on an IT course at college.
He had pretended to sympathise with Mr Thomas over a break-up with a girlfriend.
But a series of exchanges on BlackBerry Messenger and social media sites were uncovered when police raided the house in east London where Islam lived with his family, jurors were told.
Speaking to the BBC, Mr Thomas, who has learning difficulties, described Islam as a "very, very manipulative person" but said he had no intention of carrying out his requests.
He said: "He makes out he's this really kind person because that's how he comes across at first but deep inside he's evil."
Mr Thomas added: "He's not scared to go to prison, he told me that.  And he says he'll end up in a better place for the crimes he's committed. He said his God will look after him and think he's done a really good thing."
Commander Richard Walton, head of the Metropolitan Police's Counter Terrorism Command, said: "We continue to appeal to anyone who may have knowledge of people with similar intentions. The earliest we can intervene to prevent terrorism the better.
"We also remind the public that there is currently a need to protect vulnerable or impressionable adults or children from this brand of Islamic extremism."
Prosecutor Annabel Darlow QC had told the court that Islam had tried to encourage Mr Thomas to kill a soldier by telling him innocent children were being murdered by military forces.
Ms Darlow told the jury: "Thomas was a vulnerable, not particularly bright young man who was desperate to impress Islam and to try and forge some sort of friendship with him.
"Islam ruthlessly exploited to the utmost Thomas's vulnerability and obvious wish to try and ingratiate himself with Islam."
The plot was said to have been unwittingly sabotaged by Mr Thomas, who failed to buy any of the right ingredients for a bomb and revealed what was going on to "a few friends" .
Giving evidence, Islam told the jury he had talked to Mr Thomas about getting the ingredients for a bomb as an "experiment" in radicalisation and "would have told him what I was doing" if he had actually gone ahead with the purchases.
While the court heard he had also downloaded a document on explosives himself, Islam said his interest in extremism was "purely for research purposes and to understand the political side of my religion".
A teenager has been convicted of grooming a vulnerable young man after being inspired by the 2013 killing of Fusilier Lee Rigby in Woolwich.