The man, now 73, also told investigators that he tossed the body of one of the children in an incinerator when the infant died shortly after birth, said Franz Polzer, head of the Lower Austrian Bureau of Criminal Affairs.
"We are being confronted with an unfathomable crime," Interior Minister Guenther Platter said.
Authorities said three of the surviving children were confined during their entire lives to the darkness of their cell by the suspect, who Polzer said "managed to deceive everyone" until he allegedly confessed in police custody Monday.
The suspect, identified as Josef F., was an authoritarian who took care never to allow anyone near the cellar, Polzer told reporters.
The daughter, who is now 42, had been missing since 1984 and was found by police in the town of Amstetten on Saturday evening after police received a tip.
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 Monday.
"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," Polzer told The Associated Press.
Three of the surviving children lived with the grandparents and were registered with authorities. The other three apparently were held captive in the cellar with their mother, Polzer told reporters.
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.
Austrians - still scandalized by a 2006 case involving aoutside Vienna for more than eight years - expressed disbelief at the latest case.
"The entire nation must ask itself just what is fundamentally going wrong," the newspaper Der Standard said Monday in a commentary.
Guenter Pramreiter, who owns a bakery just down the street, told the AP that the suspect and his wife would regularly buy bread and rolls, though never in large quantities.
"They appeared normal, just like any other family," Pramreiter said. "I'm totally shocked. This was next door. It's terrible."
The case unfolded after a gravely ill teenager was found unconscious April 19 in the building where her grandparents live, and taken to a hospital in the town of Amstetten, about 75 miles (120 kilometers) west of Vienna. Authorities publicly appealed for her to come forward to help diagnose the young woman's condition.
After receiving a tip, police picked up the 42-year-old woman - identified as Elisabeth F. - and her father on Saturday close to the hospital.
Police said Elisabeth F. 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.
On Sunday evening, police said investigators had found the area where Elisabeth and three of the children were held captive. Investigators said the rooms were at most 1.7 meters (5 feet 6 inches) high. The area had a TV and small hot plates for cooking.
In a chronology of events outlined in a police statement, authorities said Elisabeth F. told them her father began sexually abusing her when she was 11. She told police that some years later in 1984, he sedated her, handcuffed her and locked her in the cellar.
Police said a letter written by Elisabeth had apparently surfaced a month after her disappearance, asking her parents not to search for her.
The Austria Press Agency reported that the surviving children are three boys and three girls, the youngest of whom is 5. DNA tests were expected to determine whether Josef F. is the father of the children as he claims.
Sunday's developments recalled another case that shocked Austrians in the summer of 2006, when a young woman escaped after being largely confined to a tiny underground dungeon in a quiet Vienna suburb for more than eight years.
Natascha Kampusch was 10 years old when she was kidnapped in Vienna on her way to school in March 1998. Her abductor, Wolfgang Priklopil, threw himself in front of a train just hours after her dramatic escape.
Kampusch, now 20, issued a statement Monday saying she wanted to contact Elisabeth to offer emotional and financial help.