A verdict on a third defendant, a 31-year-old Israeli man, was postponed for a mental health review.
Mohammad Abu Khdair, 16, was killed in apparent revenge for the murders of three Israeli teens in the West Bank.
The killings were part of an escalating cycle of violence, culminating in a war between Israel and militants in Gaza.
The story of two brutal killings
Interview with Mohammad Abu Khdair's mother
Mohammad Abu Khdair's body was found in a forest in West Jerusalem on 2 July 2014, two days after the bodies of the Israeli teenagers abducted and murdered by Hamas militants that June were found.
The two minors, whose names have not been released, and 31-year-old Yosef Haim Ben David were subsequently charged with Abu Khdair's murder.
On Monday, the panel of three judges at the Jerusalem District Court found the minors guilty. They will be sentenced in mid-January.
The judges found that Mr Ben David, who was portrayed as the ringleader, had participated in the abduction and murder, but said a formal verdict would be postponed until a psychiatric evaluation had been carried out.
Mr Ben David's lawyer, Asher Ohayon, submitted at the last minute a psychiatric opinion which stated that he was not responsible for his actions at the time of the murder. Prosecutors had presented evidence they said showed he was.
In their ruling, the judges determined that the three defendants abducted Abu Khdair at random as he stood on a road in the Shufat district of East Jerusalem.
The two accomplices, who were 16 at the time, then beat the Palestinian unconscious in the back of a car being driven by Mr Ben David, the judges said.
One of the minors helped douse Mohammad Abu Khdair with petrol while he was still alive, before Mr Ben David lit a match and set him on fire, they added.
The two teenagers confessed to the abduction in court, though one testified that he was not involved in the killing. Mr Ben David chose not to testify.
Mohammad Abu Khdair's father, Hussein, said Mr Ben David was trying to mislead the court.
"How can the defendant, two days ago, a year-and-a-half after the crime, bring a document claiming insanity?" he told reporters. "It's all lies and I worry that the court will free them in the end."
Prosecutor Uri Corb vowed to contest any insanity plea.
"When we try to claim that we are better than our enemies - and I think that we are better than them - we should look at this event as a mirror," he said. "As a society we will continue to fight all avengers and lynchers, as we did in this case."
Two Palestinians suspected of the murder of the three Israeli teenagers - Naftali Fraenkel and Gilad Shaar, both aged 16, and 19-year-old Eyal Yifrach - were killed by Israeli forces in a gun-battle at their hideout in Hebron in September 2014.
A third man, Hussam Qawasmeh, was sentenced to three life terms in prison in January after being found guilty by an Israeli court of several charges including three counts of accessory to murder.
Two 17-year-old Israelis have been convicted of the murder of Palestinian youth Mohammad Abu Khdair, abducted and burned to death in Jerusalem in 2014.