The body of Carina Louise Stephenson, 17, from South Yorkshire, whose family spent four months in Australia living like early settlers for the programme, was found by search teams on Saturday.
Carina was last seen on Thursday at 10am when she left h
er home at Branton, near Doncaster, on her bike.
When she failed to return home, relatives contacted the police and put posters up in the neighbourhood appealing for information.
The teenager, who had recently revealed she was a lesbian, appeared "happy and normal" in the days before her disappearance, according to her family. She had planned to start her A-levels in September before pursuing a career in the Army.
Police last night said there were no suspicious circumstances surrounding her death.
Producers of the six-part series Colony said they would decide this week whether or not to air the fly-on-the-wall after speaking to the family. It was scheduled to go out on June 6 on the History Channel.
Carina, her 13-year-old brother Tyler, father John, a 43-year-old estate manager, and mother Liz, a 38-year-old teaching assistant, volunteered for the experiment after seeing a newspaper advert.
They were chosen alongside families from Ireland and Australia to be part of a fledgling community set during the 1800-15 period.
A spokeswoman for the History Channel said: "The programme, which was a living history documentary, was filmed in August last year.
"The Stephenson family were chosen by producers because they were a very nice and likeable family.
"The Australian producer of the show, who got to know them well during their time out there, plans to speak to the family.
"Obviously the decision on whether to screen the show will depend on what the family think is best."
The programme has already been shown in Australia and is currently being screened on Irish channel RTE, which part-financed it.
The spokeswoman rejected any claims that the show itself could have led to the teenager's apparent suicide.
"The whole family came back from Australia nearly six months ago and were very positive about the experience," she said.
"They had been living the life of a convict family, along with families from Ireland and Australia, and were given a certain amount of provisions to live on.
"If there had been any upset or distress they could have left and gone home at any point. It's not Big Brother."
Yesterday Carina's parents were too upset to talk about the death of their daughter, but visited the scene, off Kilham Lane, Branton, near Doncaster, where she was found.
Police checked her computer e-mails and Internet sites for clues to her whereabouts.
At around 4pm on Saturday search teams found her body. A post mortem is due to be carried out today to establish the cause of death.
