Detective Superintendent Paul Kessell, of Dorset Police's Major Crime Investigation Team, said that police were confident that the body belonged to Gaia.
A 71-year-old woman and a 19-year-old man were released under investigation on suspicion of murder on Tuesday following their arrest the previous day.
The 19-year-old, who has epilepsy and did not leave with her medication, vanished on the afternoon of 7 November.
The discovery was made at around 3pm on Saturday by specialist search teams on land south of Swanage - close to where clothing positively identified as belonging to the teenager was found on Thursday.
"Her family have been informed and are being supported by specially-trained officers".
On Monday, Dorset police said the three people they had arrested had been released from investigation and no further action would be taken against them.
Family friend Sheri Carr, who organised the Find Gaia social media campaign, spoke of her devastation at the loss of Miss Pope. Addressing the members of the public who had gathered, Richard Sutherland said: 'I just want to say a massive thank you for coming out. Her family vowed on Sunday to get justice for her.
"Please hold on with us". You will have justice.
Gaia's sister Maya Pope-Sutherland also paid tribute in a Facebook post in which she wrote: "Can't find any words right now". I am heartbroken. I thank for my attractive twin. "Going to make her so proud".
Pope's body was found in a cliff area thick with gorse close to a beauty spot called Dancing Ledge.
Clara Pope-Sutherland called the teenager the "absolute light of my life", adding that she was "so handsome, so emotionally wise and intelligent and so passionate and artistic and creative and understanding". Part of the area had previously been searched but it is understood the spot where the body was found is particularly rugged and hard to access.
Police have discovered a body in the search for an English teenage girl who has been missing for more than a week. A member of her family has said the family will sue for wrongful arrest.
Forensic investigations have concluded at two properties in Manor Gardens, which are believed to be the homes of the 71-year-old woman and 19-year-old man who were arrested.
The force released two CCTV images of the teenager taken inside St Michael's Garage in Swanage when she bought an ice cream.