"On behalf of the family, we would really like to show how deeply grateful we are to Judge Masipa who has found Oscar not guilty of murder," said uncle Arnold Pistorius.
Pistorius was found guilty of culpable homicide and his sentencing will begin on October 13.
"We always knew the facts," he said, "and we never had any doubt in Oscar's version of this tragic incident."
Pistorius has stayed with his uncle since unlawfully killing Reeva Steenkamp on Valentine's Day 2013.
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"We respect the fact that the legal process is not over and must always be run in the course of justice."
Arnold Pistorius also expressed sympathy for the family of Steenkamp.
"It won't bring Reeva back, but our hearts still go out for her family and friends," he said "and against this backdrop we do not wish to make any further statements.