The 44-year-old was found unconscious at a residential address along with her partner Charlie Rowley, on June 30.
The pair, both in their mid-40s and reportedly with no political background to suggest they may have been deliberately targeted in an attack, are at the centre of the second apparent Novichock nerve agent incident in the United Kingdom in four months.
Assistant Commissioner Neil Basu, Britain's top anti-terrorism police officer, said the death "has only served to strengthen our resolve" to find those responsible.
The following day, South West Ambulance Service were called to the house at 10.15am and Ms Sturgess was taken to hospital.
The Salisbury hospital added that it "has seen a number of members of the public who have come to the hospital with health concerns since this incident started and none have required any treatment".
Mr Rowley is also being treated at the hospital.
Police in the United Kingdom are searching for the nerve agent that left a British couple them fighting for their lives in Salisbury.
Police identified her after the information was released to family and friends.
Laboratory tests previously confirmed that Sturgess and the man were exposed to the nerve agent after touching a contaminated item with their hands.
More than 100 police officers were deployed to try to locate a small vial believed to have contained the nerve agent that sickened the two.
He added: "This awful news has only served to strengthen our resolve to identify and bring to justice the person or persons responsible for what I can only describe as an outrageous, reckless and barbaric act".
Detectives are still working to determine the source of the contamination. "What are the authorities going to say to the parents of a young child who is contaminated with nerve gas because they were in Zizzi or The Mill last Sunday?"
The poisoning of the Skripals, both of whom spent weeks in hospital before being discharged, was blamed by the United Kingdom government on Russian Federation.
Meanwhile the investigation into the attempted murders of the Skripals is ongoing as detectives continue to assess all the evidence available.
Several sites are being searched by the local and Scotland Yard counter terrorism officers, including Queen Elizabeth Gardens in Salisbury, a property at John Baker House, Rolleston Street, Salisbury, a property on Muggleton Road, Amesbury, Boots the chemist, Stonehenge Walk, Amesbury, and the Baptist church on Raleigh Crescent, Amesbury.