Green with three of his wives
Utah Judge Guy Burningham sentenced Mr Green to serve five concurrent terms of five years for four counts of bigamy and one of failing to pay child support.
Mr Green, who has argued that his Mormon background permits polygamy, could have received up to 25 years.
He may still stand trial on a child rape charge.
Appeal
Mr Green, who will appeal against his sentence, said earlier that his prosecution had been politically motivated - part of a drive to change Utah's image ahead of the 2002 Winter Olympics.
But prosecutor David Leavitt portrayed Mr Green in court as a man driven by his ego to marry teenage girls.
The husband of five and father of 25, who lives with his family in a remote desert compound near the Utah-Nevada border, has told interviewers that polygamy is a 150-year-old part of Mormon culture and he will not give it up even if it means going to prison.
The Mormon church itself renounced polygamy in the 1890s and now excommunicates those who practice it, although some individuals and groups stand by the practice.
There are now thought to be about 30,000 polygamists in the western states of America.
Children's interests
In the run-up to sentencing, Mr Green's children sent pleading letters to Judge Guy Burningham.
"Please don't put our father in prison," wrote 10-year-old Lorin Green.
One of Mr Green's wives, Linda, argued in her letter to the judge that her husband's imprisonment would harm the children.
"Tom's children are very close to him," she wrote.
"I believe they would suffer emotionally and mentally by his being taken away.
"I worry that our children will learn to disrespect government for generations to come because of having their father sent to prison for his religious beliefs."
Besides Green's family, a family doctor, school officials and a scout leader all wrote in letters of support.
Just before sentencing, Mr Green was attending a hearing connected with his possible trial for child rape.
The charge stems from his marriage to Linda, apparently when she was 13.
She is now pregnant with her seventh child.
It is quite common among polygamists to marry off girls as young as 16.