The infants' 32-year-old mother confessed to killing them out of despair over her inability to pay the bills and the fear that having children might drive away her longtime male partner, investigators told the Austria Press Agency.
Both the woman and her 38-year-old companion were arrested and placed under formal investigation for murder.
The killings in the city of Graz, which authorities said may have begun as long as three years ago, stunned the tranquil alpine nation, where multiple homicides and other violent crimes are unusual.
The gruesome discoveries began Monday when a resident of the multifamily apartment block went to the basement to get ice cream for his children from a chest freezer shared by the building's occupants, Graz's Kleine Zeitung newspaper reported Friday. The stunned tenant discovered the dead baby, wrapped in a plastic bag, in the freezer and called police.
The authorities found a second baby at the bottom of the freezer, hidden beneath meat and vegetables.
Specially trained police dogs led investigators to the third body -- a newborn girl -- in a paint bucket that had been filled with concrete to conceal the remains, state broadcaster ORF reported.
Police searching the house and an adjacent garden shed Friday for clues to the killings came across the fourth body, which also was in a paint bucket filled with cement, hidden beneath a pile of debris in the shed, officials said.
Although police initially kept open the possibility that the infants may have been stillborn, evidence at the scene quickly pointed to the newborns' slayings before being hidden, police said.
The suspect, a bookkeeper whose name was not released in line with Austrian privacy laws, lived in the building with her partner for the past eight years, authorities said.
The suspect was not entirely coherent during questioning, but told investigators she gave birth to all the babies in her bathtub, police Lt. Col. Werner Jud said Friday.
Her partner allegedly told police he was unaware of her pregnancies and insisted he played no role in either the slayings or the hiding of the bodies.
Autopsies were held, but results had not been released as of Friday morning, officials said. They said the forensic examination was held up by the need to first slowly thaw the frozen remains of the infants found in the freezer.
DNA tests will be carried out on the woman's companion to determine if he was the father, Jud said.
Police told APA that they believed the bodies in the freezer may have been placed there as long as three years ago.
Neighbors described the woman a hard worker who kept a tidy house and a beautiful yard.
Graz, about 120 miles south of Vienna, is the birthplace of film star and California Gov. Arnold Schwarzenegger.
(AP Photo/Markus Leodolter)