The body belongs to Alisa Dmitrijeva, a 17-year-old from Wisbech, Cambridgeshire, Norfolk, who went missing in August 2011, police said in a statement Sunday.
"We are devastated by the news of Alisa's death," her family said in a statement released through local police. "We wish to grieve in private and don't want to speak with anyone from the press at this time."
The discovery of the remains on Jan. 1 launched a murder investigation.
Alisa arrived in the U.K. in 2009 from Riga, Latvia, and lived with her father, 10-year-old sister and grandmother, police said. Her mother lives nearby.
"I shall now be liaising with officers from Cambridgeshire who have been working on trying to locate Alisa in recent months as a missing person," he said in a statement. "The information they provide will give me and the team an extra focus to the inquiry."
Cops said late last week that they are concentrating on a two-month period last fall and appealing for those who may have been in the area (part of the Queen's vast 20,000 acre estate) around that period to get in touch.
"We are still trying to establish any activity which took place on or around the site during the time frame of the end of August to the end of September 2011," Fry said. "We would like to identify people who may have worked in that area or were involved in organizing or running any specific events that may have taken place."
Alisa was last seen getting into a green Lexus with two male friends after midnight on Aug. 31. Her grandmother reported her missing about six days later.
Through an interpreter, her grandmother spoke to the U.K.'s Times newspaper Saturday.
"There have been so many days, wondering where she is, and what has happened, I don't know what to think any more," she said. "One day you have someone in your life, the next you don't. Then it feels like they are never there."