Fourth District Judge Donald Eyre took just 30 minutes to find Green guilty for his relationship with Linda Kunz, who is now his legal wife. The non-jury trial lasted about an hour.
The judge had already rejected defense arguments that the statute of limitations had run out and that the case should be thrown out because the alleged rape didn't take place in Utah.
Green's sentencing is scheduled for Aug. 16; he faces up to life in prison.
Green, who has four other "wives" and 30 children in all, including seven with Kunz, already is serving a five-year sentence for bigamy and criminal nonsupport. He was convicted in May 2001.
Kunz was called to the stand Monday morning but refused to testify. Spouses do not have to testify against each other.
"We don't feel like this was a crime," she said after the verdict.
Prosecutors submitted her testimony from previous hearings, as well as her 1973 birth certificate and the 1986 birth certificate of the couple's first child, Melvin.
"Basically, this case comes down to math," Eyre said. "We know a normal human gestation takes nine months."
After prosecutors rested their case, defense attorney John Bucher moved to have the charge dismissed. Eyre rejected the request, and Bucher then rested his defense without presenting any evidence. He said the case gave him several avenues for appeal.
The defense had acknowledged that Green got Kunz pregnant when she was a minor, but had argued that Utah prosecutors had no jurisdiction to bring a the child rape case because the child was conceived during a Mexican honeymoon.
Eyre had ruled that even though prosecutors couldn't prove the alleged rape took place in Utah, he agreed with prosecutors that Green hatched a conspiracy in Utah to marry the girl.
"I have tremendous empathy for Tom Green, for his children, for his family. But the consequences of criminal conduct -- whether it's child rape, bigamy or drugs is that there are always secondary victims," said prosecutor David Leavitt.
Polygamy, advocated by the Mormon Church early in its history, is an open secret in Utah and elsewhere in the West, where there are an estimated 30,000 people practicing plural marriage.
But Green practically dared prosecutors to go after him by appearing on TV talk shows such as Sally Jesse Raphael's, saying that his lifestyle was a constitutional right.
On Monday, prosecutors concluded their case by playing a video clip from a January 2001 "Dateline NBC" interview. In it, Green admitted that his only defense to the rape charge was challenging the state's jurisdiction in the case or the statute of limitations. Both were dismissed by the judge.
"It underscores our thought all throughout the case that Tom Green was our best witness. It's harder to convict somebody when there's no videotape," Leavitt said.
Juab County Attorney Leavitt, Gov. Mike Leavitt's brother and himself a descendant of plural marriage, took the extraordinary step of prosecuting the polygamist for bigamy.
Members of the Church of Jesus Christ of Latter-day Saints abandoned polygamy in the 1890s, when church leaders renounced it as a condition for Utah statehood. Polygamists are excommunicated from the church.