The Gloucester coroner is writing to the relatives to tell them they can now go ahead with funeral arrangements, said a police spokesman.
"This is sure to be of great comfort to the families. It will be an important stage in coming to terms with their loss."
The formal release of the remains by Gloucester district coroner David Gibbons had been delayed by West's change of lawyers and other factors.
Mr Gibbons said: "The reasons for the delay are best known to those who were defending Mr West.
"On the advice of counsel they were unable for some time to give permission and I have unfortunately been unable to release them.
"I had hoped to get that permission much earlier but it was not to be."
Mr Gibbons had earlier confirmed he would now be holding full inquests into three of West's alleged victims as a result of the builder's death in his cell at Winson Green prison in Birmingham on Sunday.
The inquests will be those of his first wife Catherine, their daughter and nanny, with whose murders West alone was charged.
The deaths of the other nine victims - all found buried at 25 Cromwell Street - still remain the subject of murder charges against West's 41-year-old wife Rosemary.
Committal proceedings ware scheduled for next month, at which Mrs West's lawyers are expected to argue that the charges should be dropped. Inquests on the 12 victims were formally opened and adjourned for identification purposes and to establish the cause of death.But Mr Gibbons adjourned the hearing to a full inquest after court proceedings are completed.
Joan Owen, the mother of one of the victims, Alison Chambers, said of the coroner's decision: "This is the news we have been waiting for. It's a great release."
Mrs Owen, 52, of Port Tennant, Swansea, added: "After the confirmation that Alison was one of the victims, it was the wait for her body that caused the most hurting."
The circumstances surrounding the death of West, who was charged with the murders of 12 young women and girls, are being investigated separately by the Prison Service and the police.