Morena Petrus Mofokeng of Paballong Village in QwaQwa was convicted by the High Court presiding at Thabo Mofutsanyana District Justice Centre in Phuthaditjhaba on Tuesday.
Police spokesperson Mmako Mophiring said Mofokeng broke into the house of the 50-year-old woman and raped and killed her in October 2012. DNA evidence taken from the scene linked him to the rape of his own 85-year-old grandmother in October 2010.
His grandmother died a week after the attack and the case was provisionally withdrawn due to a lack of evidence at that stage. But, the charges were re-instated when DNA evidence proved he was her assailant.
He will be sentenced on two counts of rape, and one count of murder on Thursday.