An FBI agent says the three women found alive in Cleveland, Ohio, a decade after going missing have provided the ultimate definition of survival and perseverance.
The women were freed after Amanda Berry, who disappeared over 10 years ago when she was 16, attracted the attention of a neighbour on Monday evening.
Gina DeJesus, who went missing aged 14 a year later, and Michelle Knight, who vanished in 2002 aged about 19, were also rescued from the property.
Deputy Police Chief Ed Tomba said a girl, six, also rescued from the house was believed to be the daughter of Ms Berry.
The three women were taken to hospital for a check-up and to be reunited with their relatives before being discharged on Tuesday morning.
FBI Special Agent Stephen Anthony said:
"The nightmare is over. These three young ladies have provided us with the ultimate definition of survival and perseverance. The healing can now begin."
Ariel Castro, 52, a school bus driver, is under arrest, as are his brothers Pedro, 54, and Onil, 50.
"We believe we have the people responsible," Deputy Police Chief Tomba said.
Police believe they were at the house the entire time they were missing. The BBC reports neighbours said they did not realise anybody was living at the house at 2207 Seymour Ave.
Cleveland mayor Frank Jackson said many questions need to be answered.
The women's families have responded with stunned joy. Sylvia Colon, a relative of Gina DeJesus, said they had never given up hope.
But Ms Berry's mother, Louwana, died in March 2006, three years after her daughter went missing. A local politician said the mother had died of a "broken heart".
In an extraordinary twist, it emerged that Ariel Castro's son - also called Ariel, although he goes by his middle name Anthony - wrote an article about the disappearance of Gina DeJesus for a newspaper in 2004.
The BBC says police have not commented on the case of a fourth missing girl, Ashley Summers, who disappeared in the same area in July 2007. She was aged 14 years.