Captain Kay Makhubela said the suspects were arrested during Wednesday evening for the murders of Gregory Naidoo, 57, Melanie Naidoo, 51, and her daughter Rakiel Naidoo, 23.
The three went missing on Sunday night in what was believed to have been a robbery at their home in Northcliff. Their bodies were found bound and gagged in Centurion on Monday.
"We have identified the bodies by what remains of our family, clothes and other body parts. We have made no facial recognition and are still waiting on the results from all the testing that has been done," Shaniel Naidoo said.
News24 reported on Tuesday that the family had confirmed that the remains were their relatives.
Police are still awaiting DNA results.
Makhubela said one of the suspects is a believed to be a former employee.
"He has worked for the family for more than 12 years. If there are any suspects to be arrested, they will be," he said.
Police have recovered the family vehicle and stolen property.
They face charges of murder, kidnapping, unlicensed firearm, house robbery and in possession of stolen vehicle and property.
They are expected to appear in Johannesburg Magistrate's Court on Friday. -- News24