Mahlangu killed Terre'blanche over a pay dispute in April 2010 at the white farmer's home in Ventersdorp.
Judge John Horn said the attack was not racially motivated.
Terre'blanche, a burly man known for his thick white beard and fiery rhetoric, led the hardline supremacist Afrikaner Resistance Movement, known by its Afrikaans acronym AWB.
Its members adopted military uniforms and flags with a symbol reminiscent of the Nazi swastika, and called for an all-white homeland in post-apartheid South Africa.
A small group of his armed supporters attempted a coup in the black-run "homeland" of Bophuthatswana shortly before the first all-race elections in April 1994 but retreated after meeting resistance from security forces.
Graphic images of three AWB men being shot dead on a road by a Bophuthatswana policeman at point-blank range marked the end of any AWB pretensions to be a serious military force.
A second man, who was a minor at the time of Terre'blanche's murder, was found guilty of housebreaking in Ventersdorp and given a suspended sentence.
Prosecutors said Mahlangu and his co-accused broke into Terre'blanche's home, where they found the 71-year-old asleep and hacked him to death with pangas and pipes. – Reuters