Boniadi and Cruise first met in November 2004, and their first date included a tour of the Empire State Building, dining at an upscale sushi restaurant and private ice skating at Rockefeller Center, according to the article.
The couple became inseparable as Cruise groomed her, according to Orth, including allegedly wanting "Boniadi's incisor teeth filed down."
Boniadi, the magazine says, "first sensed that this was possibly going to be an arranged marriage," and although they spent that first night together, "they did not have sex."
Vanity Fair reported that Cruise told Boniadi, "I've never felt this way before," and eventually his affection became "overwhelming" for the actress.
At one point, Cruise complained to Boniadi, "I get more love from an extra than from you," according to Vanity Fair.
Cruise also believed that Boniadi wasn't sufficiently respectful enough of David Miscavige, Orth said.
The relationship ended in January 2005, the magazine reported, three months before Cruise appeared in public with Katie Holmes. The article claims that Cruise wanted "someone with her own power, like Nicole Kidman."
Asked on "GMA" whether there were any photos of Cruise and Boniadi, Orth said that sources told her that photos of the couple "were taken away, and they no longer exist."
Boniadi, the magazine writes, was then reportedly sent to a Scientology center where she broke down and revealed her relationship with Cruise to a friend, which supposedly violated her confidentially agreement. As punishment, Vanity Fair says, her chores included "scrubbing toilets with a toothbrush, cleaning tiles with acid and digging ditches in the middle of the night."
The Church of Scientology, however, denied this to the magazine, saying, "The Church does not punish people, especially in that way."
Oscar-winning director and former Scientologist Paul Haggis supports Vanity Fair's story that Boniadi was auditioned by the church to be Cruise's real-life girlfriend.
In an email to ShowBiz411.com, the "Crash" director says he has known Boniadi for three years.
"Naz was embarrassed by her unwitting involvement in this incident and never wanted it to come out, so I kept silent," Haggis wrote in the email published on the website Sunday. "I was deeply disturbed by how the highest ranking members of a church could so easily justify using one of their members; how they so callously punished her and then so effectively silenced her when it was done."
Karin Pouw, a spokeswoman for the Church of Scientology International, said Haggis is an "apostate." She told ABC News Tuesday that Haggis is "attempting to grab headlines and falsely slander his former religion."
Orth's story is in the October issue of the magazine, which features Holmes on the cover and will hit newsstands in New York and Los Angeles Thursday. A rep for Holmes told ABC News that the Vanity Fair story was done without her participation.