The court found Dirk Coetzee, former commander of a covert police assassination squad who later joined President Nelson Mandela's African National Congress (ANC), and former policemen Almond Nofomela and David Tshikalanga guilty of stabbing Mxenge to death in a deserted sports stadium.
Mxenge represented many ANC members while the organisation was banned under apartheid laws.
Coetzee was the first white policeman involved in covert operations against the ANC to turn on the apartheid system and publicly reveal details of the state campaign against the organisation.
The three former policemen are among more than 6,000 South Africans who have applied for amnesty under a National Unity and Reconciliation Act designed to heal the wounds of apartheid.
A decision on their applications could be expected in mid-June, Coetzee's lawyer, Julian Knight, said. Sentencing was postponed to 1 July to give the defence teams time to prepare their arguments for mitigation.
Passing judgment, Judge Piet Combrinck told the packed court that confessions made by the three men to a 1990 commission investigating police hit-squads could be used against them. He said the failure of the accused to take the stand to refute their confessions meant that they had told the truth about their involvement in killing Mxenge.