They say three of the children "never saw sunlight" until they were freed over the weekend.
Police in the town of Amstetten, west of Vienna, say the suspect, 73-year-old Josef Fritzl, has confessed, but that he had previously "managed to deceive everyone".
He allegedly kept them prisoner in his cellar, and police official Franz Polzer says he told investigators that he tossed the body of one of the children in an incinerator after the child died.
Reporters were told today that the man's daughter and her children have been placed in psychiatric care.
The 42-year-old, Elisabeth Fritzl, had been missing since August 29 1984. She was found by police in the town of Amstetten on Saturday, after police received a tip-off.
"We are being confronted with an unfathomable crime," said interior minister Guenther Platter.
Three of the children, aged 19, 18 and 5, had been locked up in the basement with Ms Fritzl since birth and never seen sunlight, police said, raising worries about their physical and mental state. The younger two were boys, the eldest a girl.
Three other children - two girls and one boy - were brought up by Fritzl and his wife.
All the victims are receiving medical treatment, said police. State prosecutors said Fritzl would be summoned before a judge later.
Investigators spent the day examining the cells where the victims had allegedly been held captive. Forensic experts in white uniforms and gloves carried out boxes of evidence from the house which is on a busy street with shops.
Fritzl had hidden the entrance to the cell behind shelves and only he knew the secret code for the reinforced concrete door, said officials.
Photographs showed a narrow passageway leading into other rooms which included a cooking area, sleeping area and a small bathroom with a shower. A tube provided ventilation.
Austrians - still scandalised by a 2006 case involving a young woman who was kidnapped and imprisoned in a basement cell outside Vienna - expressed disbelief that something similar could happen.
Natascha Kampusch, then 10 years old, was snatched from another small town in Austria, Strasshof, in 1998, and kept imprisoned for eight years.
Residents of the middle-class district said nothing in their contacts with the family suggested what allegedly was happening in the basement.
The suspect "was friendly - that's why this is so unbelievable", said Franz Redl, 56, who owns a shop across the street. "I'm sure the authorities did all they could. He planned everything so perfectly."
In a chronology of events outlined in their statement, police said that Miss Fritzl told them her father began abusing her when she was 11.
Police said she alleged that, some years later, on August 28 1984, he sedated her, handcuffed her and locked her in a room in the cellar in Amstetten.
Police said a letter written by Miss Fritzl had apparently surfaced a month after her disappearance, asking her parents not to search for her.
Police said Miss Fritzl alleged that, during the 24 years that followed, she was continually abused by her father and gave birth to six children.
"Elisabeth Fritzl taught them how to speak," Mr Polzer said.
In 1996, she gave birth to twins, police quoted Miss Fritzl as saying. But one died several days later because it was not properly cared for, according to police, who said they are investigating.
Mr Fritzl apparently removed the body from the cellar and burned it, the police statement said. It was not immediately clear if the twin who allegedly died was included in the police total of six children.
Police said three of Miss Fritzl's children were registered with authorities and lived with the grandparents in an apartment in the house.
According to the police statement, Josef Fritzl and his wife, Rosemarie, had told authorities they had found those children outside their home in 1993, 1994 and 1997.
Fritzl was an authoritarian who took care never to allow anyone near the cellar, Mr Polzer told reporters.
Police released several photos showing parts of the cramped basement cell, with a small bathroom and a narrow passageway leading to a tiny bedroom. Investigators said an electronic keyless-entry system apparently kept the daughter from escaping from the cell, which was made of solid reinforced concrete.
The suspect was expected to appear in court later today.
"He admitted that he locked his daughter, who was 18 at the time, in the cellar, that he repeatedly had sex with her, and that he is the father of her seven children," Mr Polzer said.
Hans-Heinz Lenze, a senior local official, said the suspect's wife apparently had "no idea" of what went on and was devastated.
"You have to imagine that this woman's world fell apart," he said.
After receiving a tip, police picked up the 42-year-old woman and her father on Saturday, close to the hospital.
Police said the woman appeared "greatly disturbed" during questioning. She agreed to talk only after authorities assured her she would no longer have to have contact with her father and that her children would be cared for.
Former captive Ms Kampusch, now 20, issued a statement today saying she wanted to contact Elisabeth to offer emotional and financial help.
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