The device failed to detonate but prosecutors said the actions of 20-year-old Damon Smith on October 20 last year were "incredibly dangerous".
Smith constructed the device in the kitchen of his mother's home after reading a magazine published by Al-Qaeda.
He packed it into his rucksack and left it on a carriage on the Jubilee Line at Southwark Station on his way to college.
Passengers noticed the bag and alerted the driver, who initially thought it was lost property before spotting wires and raising the alarm.
A jury at London's Old Bailey court convicted him of possession of an explosive substance with intent to endanger life or cause serious injury.
A psychiatric report read out in his defence confirmed that Smith was on the autistic spectrum.
It found he had been interested in bomb-making since the age of 10, saying it was "something to do when he was bored".
"Although he claimed this was a prank, the bomb he left on the train was clearly designed to cause horrific injuries."
Smith, who was 19 at the time, was tracked down though CCTV footage.
A police search at his home in south London revealed a fixation with guns and explosives, including a picture of Smith with guns entitled "2016 an Islamic State fighter" found on his laptop.
His lawyer, Richard Carey-Hughes, told the court that Smith was not a "hate-filled jihadi" and that if he had wanted to make an effective bomb, he would not have made such a "shoddy, ineffective device".
Smith, who faces several years in jail, will be sentenced on May 26.
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