Officers said the discovery was made at a house in the Barton Hill area last night.
"The information suggested that Becky's body had been cut up and a search at the new location resulted in the discovery of body parts," Detective Superintendent Mike Courtiour said.
"As a result of this latest development, a further four men and a woman have been arrested on suspicion of assisting an offender.
"They remain in police custody at this time as do the man and the woman arrested on suspicion of Becky's murder.
"This is devastating news for Becky's family and friends and our thoughts are with them. We will continue to offer every support we can to them during this terrible ordeal."
The teenager had been missing for 12 days. Her family says it's devastated by the development.
"We are at an utter loss to understand why anyone would want to hurt our beautiful Becky in such a brutal way," Becky's mother Tania, grandmother Pat and brother Daniel said in a statement.
Christian bereavement counsellor Barbara Pymm told Premier it was a tragedy and the family would take some time to grieve.
"We pray that God will meet them, that they will find His comfort, His peace and a wonderful thing is that we have a peace which is beyond our understanding.
"And we can pray for that when humanly we would say 'well how can there be peace in this situation?' but we know a God who is big enough to bring peace in the very worst."
A 28-year-old man and a 21-year-old woman have been arrested on suspicion of her murder and are in police custody.