Police were first called to Carlton Cemetery, Barnsley, at 2.52 pm on Monday, May 2, by a passer-by, and officers found a "disturbance to a grave" and later confirmed that it wasn't part of any "pre-planned activity”.
Police tents could be seen at the cemetery for several days as officers worked.
Officers today revealed that a body had to be exhumed as a result of the investigation, with a private re-burial service carried out for the family this morning.
The family of the woman whose grave was disturbed has paid tribute to the specialist teams involved in the case, which is still under investigation.
In a statement, they said: "The family would like to thank each and every person that has been involved in this horrific case, for the work that has been necessary and for the work that needs to continue.
"The support we have received and the respect for us and our loved ones that have been disturbed has been beyond anything anyone could imagine.
"There are not many angels in this world but each and every person that has been involved are just that - angels.
"They have gone above and beyond their duty. As a family we have so much respect for them and they should be recognised for their work.
"The family now request privacy to grieve for our loved ones."
Police have been working closely with the local authority and specialists since May 2, when the disturbance was reported to them.
The grave was the final resting place of two members of the same family. Officers say the woman's body was ‘carefully and sensitively exhumed’ as part of enquiries to examine the circumstances surrounding the disturbance. This work has now concluded.
DCI Andrea Bowell, the senior investigating officer, said: "The family connected to this grave has been kept regularly updated on the work we have been carrying out. It has been an extremely sad and distressing time for them and I would like to thank them for their support and understanding while we carried out our enquiries. They have my sincere condolences.
"I would also like to thank members of the wider community for their patience – I know people have been unable to visit their loved ones while we have been on-site and I am grateful for your understanding."
The woman's reburial took place during a private service at the cemetery earlier today, Friday, May 13. Flowers were laid on her grave and also on the neighbouring graves which were affected by the work, as a token of thanks and respect.
The investigation remains ongoing. Anyone who saw any unexplained or unusual activity at the cemetery in the time leading up to May 2 is asked to contact the police on 101 quoting incident number 559 of May 2 .
Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website Crimestoppers-uk.org or by calling their UK Contact Centre on 0800 555 111.