A woman who was 15 when she disappeared from her home 10 years ago has been reunited with her family after telling police she was kidnapped by her mother's ex-boyfriend who sexually assaulted her, forced her to marry him and fathered her child.

Police in Santa Ana, California, arrested Isidro Garcia, 41, on suspicion of kidnapping for rape, lewd acts with a minor and false imprisonment.

Police described a decade during which the victim - abused mentally, physically and sexually by her captor - was moved at least four times and given multiple fake identities to hide her from family and authorities.

Garcia allegedly told her that her family had stopped trying to find her and that if she tried to contact them they would be deported.

"Even with the opportunity to escape, after years of physical and mental abuse, the victim saw no way out of her situation and lived a life with Garcia under sustained physical and mental abuse," a police statement said.

Neighbours were stunned, describing them as a seemingly happy couple who doted on their young daughter and liked to host parties at their apartment in the working-class community of Bell Gardens, about 20 miles from where she originally disappeared.

"He treats her like a queen. He does his best to do whatever she wants," next-door neighbour Maria Sanchez said in Spanish.

The woman, now 25, whose identity is not being released, first contacted authorities on Monday - the same day Garcia was first arrested. Police said she came forward after finding her sister on Facebook.

Corporal Anthony Bertagna of Santa Ana police said his department had established that the girl arrived from Mexico in February 2004 to join her mother and sister in Santa Ana, about 30 miles south east of central Los Angeles. She had entered the United States illegally and spoke no English.

Garcia was her mother's boyfriend and after a fight between the girl's mother and Garcia in August 2004, the mother left the house and the girl went to a nearby park. Garcia followed the girl and when he caught up with her she said she had a headache and wanted to go home.

He began threatening the girl and gave her five pills that he said would help her headache - but instead knocked her out.

When the girl awoke, she was locked in a garage in Compton, a city between Santa Ana and Los Angeles.

The mother "filed a police report and for 10 years (police) did due diligence. But they were changing their names and dates of birth and physical locations so that made it exceedingly difficult", Cpl Bertagna said.

In 2007 Garcia obtained documents from Mexico that gave the girl a new name and date of birth. Using them, he married her at a courthouse and fathered a girl with her in 2012.

Garcia secured two jobs for them on a night cleaning crew so he could keep watch over her. She tried to escape twice but was severely beaten.

Recently, she found her sister on Facebook and they started to communicate. She also learned that her mother had indeed tried to find her, going to a Spanish-language television station and newspaper in 2004.

She started reflecting on her own child's situation and realised she needed to leave, Cpl Bertagna said. On Monday, she went to police in Bell Gardens and reported that she was a victim of domestic abuse. She also told them of her abduction.

Police arrested Garcia on Monday during a traffic stop in Bell Gardens. Yesterday Santa Ana police arrested him on kidnapping and other charges and also interviewed him.

Garcia is expected to be arraigned today.

Neighbours near Garcia's apartment in Bell Gardens said they knew him as Tomas Medrano and described him as a devoted family man who worked hard to provide for his wife and three-year-old daughter.

They said he worked at a food-service company while she was a caretaker at a nearby business. The couple attended church a block away and were known for parties where they would hire mascots and hold a raffle for children in the neighbourhood.

"I'm astounded she waited so long to say something," said Rita Salazar, who lived opposite the couple and said she never saw any signs of trouble.

The case comes just over a year after kidnapping and rape victims Amanda Berry, Gina DeJesus and Michelle Knight, three women who had gone missing separately about a decade earlier while in their teens or early 20s, were rescued from a house in Cleveland, Ohio.

Elizabeth Smart, who was kidnapped from her Utah bedroom at 14 and held captive for nine months, said she was "so happy" to hear of the woman's rescue.

Ms Smart, now 26, said people could not know what victims were going through and should not question why the woman did not escape sooner.

"We don't know what these evil people are holding over them - whether it's their families' lives, their lives, whatever it is," she said. "We just don't know."

A prominent psychiatrist who helped define Stockholm syndrome, in which victims of abduction begin to sympathise with their captors, said determining why a victim resists possible escape even when an opportunity is available is not an exact science.

Dr Frank Ochberg said the relationship could sometimes involve a "trauma bond", whether a physically abusive marriage or a kidnapping victim.

People in this situation become "infantilised, dominated. They end up being attached to the person who dominates them, much like a child," he said.

But in other cases, it can be more rational. "They know the risks of escape, and they don't want to take the risk," Dr Ochberg added.