"We are in a state of total shock - firstly about the tragic death of Reeva who we had all got to know well and care for deeply over the last few months," Anthony Pistorius said in a statement released by his nephew's agent.
"They had plans together and Oscar was happier in his private life than he had been for a long time," he said.
Pistorius, 26, was charged on Friday with murdering Steenkamp in the early hours of the previous day. He broke down during a 40-minute bail hearing at a Pretoria court but was not asked to enter a plea.
Prosecutors alleged the shooting was premeditated - a charge that could put Pistorius behind bars for life if he is convicted.
Anthony Pistorius reiterated the family's belief that the track star - a double amputee who became one of the biggest names in world athletics - had not deliberately shot Steenkamp, a 30-year-old model. Initial reports suggested he may have mistaken Steenkamp for an intruder.