Gary Dobson and David Norris are to be sentenced as juveniles for the racist murder of black teenager Stephen Lawrence, as they were aged 17 and 16 at the time of the killing.
Mr Justice Treacy said the murder was a "terrible and evil crime" as he began sentencing the pair at the Old Bailey on Wednesday.
He said the evidence did not prove that either defendant had a knife, but it was used with their knowledge or approval, Sky News reported from the court. But he said the sentence may be lower "than some expect".
Dobson and Norris, now 36 and 35 respectively, were found guilty by a jury on Tuesday, nearly 19 years after Lawrence was killed.
The 18-year-old was fatally stabbed by a gang of white youths in a racist attack in Eltham, south east London.
The starting point for Dobson and Norris's sentences is 12 years because of their age at the time of the attack.
However Mr Justice Treacy will take into account the fact that the murder was racist, and that the pair realised that one of their group might use a knife.
Scotland Yard Commissioner Bernard Hogan-Howe welcomed the convictions but said the police were still hunting the other people involved in the attack.
"The other people involved in the murder of Stephen Lawrence should not rest easily in their beds," he warned on Wednesday.
Yesterday Mr Lawrence's parents spoke of their joy and relief at the verdict, but mother Doreen said it was not an occasion for celebration.
Speaking outside the Old Bailey, with her voice breaking at times, she said: "Despite these verdicts, today is not a cause for celebration. How can I celebrate when my son lies buried, when I cannot see him or speak to him?
"When I will not see him grow up or go to university, or get married or have children. These verdicts will not bring my son back.
"How can I celebrate when I know that this day could have come 18 years ago if the police, who were meant to find my son's killers, (had not) failed so miserably to do so?"
In a statement read by his solicitor Jocelyn Cockburn, Neville Lawrence said: "My life was torn apart by the senseless murder of my son over 18 years ago.
"Unfortunately no one was brought before a court at that time, as they should have been.
"The loss itself together with the lack of justice have meant that I have not been able to rest all this time.
"I am therefore full of joy and relief that today, finally, two of my son's killers have been convicted for his murder."
Later in his statement, he said: "I'm also conscious of the fact that there were five or six attackers that night. I do not think I'll be able to rest until they are all brought to justice."
Speaking to Channel 4 News, the murdered teenager's father called for Norris and Dobson to name the rest of those responsible for his son's murder.
"I'm praying that these people now realise that they have been found out and say to themselves: 'Yes I did that awful deed, but I wasn't alone in that action that night and there are other people who are also guilty of what I have done' and name them," he said.
Neil Acourt, Jamie Acourt and Luke Knight were arrested along with Norris and Dobson in 1993 in connection with Mr Lawrence's murder.
The original investigation into the murder came under criticism by a public inquiry, which branded the Metropolitan Police institutionally racist.
More than a decade later, after successful convictions in cold cases including Damilola Taylor, a team of forensic scientists was called in to look again at the Stephen Lawrence evidence.
They discovered tiny amounts of blood, hair and fibres on clothing seized from Dobson and Norris' homes, which led to a successful prosecution.
The pair have continued to protest their innocence despite yesterday's guilty verdicts.