Gary Dobson and David Norris were found guilty by an Old Bailey jury after a trial based on forensic evidence.
The two men will be sentenced as juveniles because they were under 18 at the time of the attack, which happened in south-east London in April 1993.
Police say the investigation could be reopened if new evidence emerges.
Gary Dobson, 36, and David Norris, 35, can expect to receive sentences considerably shorter than would an adult convicted of the same crime under today’s laws.
Reports say they could serve minimum prison terms of around 12 years each.
Scientists found a tiny bloodstain on Gary Dobson’s jacket that could only have come from Stephen Lawrence. They also found a single hair belonging to the teenager on David Norris’s jeans.
Acting Deputy Commissioner of the Metropolitan Police, Cressida Dick, who ordered the 2006 cold case review that led to the convictions, acknowledged that police believe there were five people involved in the murder, but there are currently no “live” lines of inquiry.
“If there was an opportunity to bring the other people who were involved in that night to justice, we would do so,” she said.
In a statement read by his lawyer outside the Old Bailey on Tuesday, Stephen Lawrence’s father, Neville Lawrence, said the convictions were a moment of joy and relief – but he could not rest until all of those who killed his son were brought to justice. He described the investigation and preparation of the case as “faultless”.
The father later told Channel 4 News: “I’m praying that these people now realize that they’ve been found out and say to themselves, <<yes I did this awful deed, but I wasn’t alone in that action that night and there are other people also guilty of what I’ve done>> and name them.
“I hope before the sentence is passed, they will talk and give the rest of these people that killed my son up.”
The original failed investigation into the murder led to the Metropolitan Police being branded as institutionally racist.
Police identified five men who were later named in a damning public inquiry as the “prime suspects”.
By that time, there had already been a catalogue of police errors and two failed prosecutions, one brought by Stephen Lawrence’s parents.
In a four-year-long cold case review, a fresh team of forensic scientists uncovered microscopic evidence linking two of the five men to the murder – evidence that the police had held all along.
The material – bloodstains, clothing fibres and a single hair belonging to the teenager – were recovered from the clothes of the suspects which had been seized in 1993.
Scientists recovered the material using advanced techniques which were not available to the original case scientists.
Gary Dobson and David Norris denied the murder. They said their clothing had been contaminated as police mixed up evidence over the years. Detectives spent months establishing the movements and handling of the exhibits since 1993 – and the jury were told that contamination was implausible.
Gary Dobson, who was jailed for five years in 2010 for drugs trafficking, is among a small number of men to have been tried twice for the same crime after the Court of Appeal quashed his 1996 acquittal for the murder.
David Norris was convicted in 2002 of a separate allegation of racially threatening behavior.
In mitigation, ahead of sentencing on Wednesday, counsel for Gary Dobson said there was no evidence he had been the leader or prime motivator of the group that attacked the teenager.
David Norris’s counsel repeated his client’s pleas of innocence – and revealed his client had been beaten up while on remand at Belmarsh prison, suffering a broken nose and four broken ribs.
Justice Treacy discharged the jury and thanked them for their “dedicated service”. He told them the public owed them a debt of gratitude.
Prime Minister David Cameron said: “In the 19 years since his murder, Stephen Lawrence’s family has fought tirelessly for justice.
“[The] verdict cannot ease the pain of losing a son. But, for Doreen and Neville Lawrence, I hope that it brings at least some comfort after their years of struggle.”
Matthew Ryder QC represented the Lawrence family in its civil claim against the police. He told BBC Radio 4’s Today programme that the Lawrence case was a “Rosa Parks moment” for British society.
“It was a moment when you saw the victims of injustice fighting for justice and the system letting them down and I think for that reason it profoundly changed how we view race and racism within this society,” Matthew Ryder said.
“On the face of it – it was a crude, violent form of racism – which every reasonable person would condemn – but what followed on from that, what’s always been part of the Lawrence case, was the pernicious, systemic forms of racism which caused the investigation to fail.”
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