Amanda Berry, who disappeared in 2003 aged 16, escaped with a neighbor’s help while her alleged captor, later identified as Ariel Castro, was away.
Gina DeJesus, who went missing aged 14 a year later, and Michele Knight, who vanished in 2002 aged about 19, were also rescued from the property.
School bus driver Ariel Castro and his two brothers have been arrested.
The three women were taken to hospital for a check-up and to be reunited with their relatives before being discharged on Tuesday morning.
A six-year-old girl also rescued from the house was believed to be the daughter of Amanda Berry, Deputy Police Chief Ed Tomba told a news conference.
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.”
“Yes, law enforcement professionals do cry,” he added.
Ed Tomba vowed prosecutors would “bring the full weight of justice” on those responsible in the “horrific case”.
Ariel Castro, 52, and his two brothers, Pedro, 54, and Onil, 50, have been taken into custody.
Police Chief Michael McGrath said the women were believed to have been tied up at the house. Officials said they may also investigate other properties.
Amanda Berry, now 27, escaped on Monday evening when a neighbor heard her screaming and kicking a door, while her alleged captor was out of the house.
Rescuer Charles Ramsey said he had helped kick in a metal door so that Amanda Berry could climb outside and phone police.
In a recording of Monday’s emergency call, Amanda Berry says: “I’ve been kidnapped, and I’ve been missing for 10 years. And I’m here. I’m free now.”
Amanda Berry identifies herself to the 911 dispatcher, saying she has been on the news for the past decade, and begging for help to arrive before her captor returns.
Police Chief Michael McGrath told Tuesday’s news conference: “Thankfully, due to Amanda’s brave actions these three women are alive today.”
Neighbor Anna Tejeda said she had refused to believe the young woman at first.
“You’re not Amanda Berry. Amanda Berry is dead,” she said, according to the Associated Press news agency.
Other neighbors in the working-class district said they did not realize anybody was living at the house at 2207 Seymour Ave.
During the news conference, Public Safety Director Martin Flask said that in March 2000, Ariel Castro had called the authorities to report a fight on his street, but no arrest was made.
In January 2004, police called at Ariel Castro’s home, but no-one answered. They were alerted by children’s services after a child was left at a depot on a school bus that Ariel Castro had been driving. Authorities concluded there had been no criminal intent.
Amanda Berry had last been heard from aged 16 when she called her sister on 21 April 2003 to say she would get a lift home from her job at a Burger King restaurant.
In 2004, Gina DeJesus – who is now 23 years old – was believed to have been on her way home from school when she went missing.
Their disappearances made local headlines in Cleveland, and many assumed the girls were dead.
The case of Michele Knight, who was older than the other women when she disappeared and is now 32, was less widely publicized.
Her grandmother, Deborah Knight, was quoted by the Cleveland Plain Dealer newspaper on Monday as saying the authorities concluded she had run away.
The victims’ families have responded with stunned joy. Sylvia Colon, a relative of Gina DeJesus, said they had never given up hope.
But Amanda 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 his local newspaper in 2004.
Police have not commented on the case of a fourth missing girl, Ashley Summers, who disappeared in the same area in July 2007 when 14 years old.
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