Police found the babies on Sunday in Wenden, a town in the German state of North Rhine-Westphalia, after their 44-year-old mother turned herself in to police accompanied by her husband and two of her adult children, police spokesman Matthias Giese told The Local.
The woman's 18-year-old son and 24-year-old daughter found the dead babies while searching through expired food for a frozen pizza, according to investigators. The bodies were wrapped in towels inside three bags.
"We believe it happened around 1988 because one of the babies was wrapped in a 1988 newspaper," Giese said.
The siblings confronted their parents on Sunday evening, after the couple returned from a trip to the Black Forest, and the family members went to police together. A 23-year-old son also lives in the Wenden home.
"The woman is in psychiatric care now and is being watched by police," Giese said.
The babies were likely born living, district prosecutors in Siegen told German press agency DPA.
The mother, who faces arrest on suspicion of murder, told police she felt "deeply guilty," German press agency DDP reported.
The woman is believed to have hidden the three pregnancies from her family, giving birth in the bathtub and then placing the newborns in plastic bags, where they suffocated, before hiding them in the freezer.
"The crime is basically solved," a spokesman of the prosecutors' office told DPA.
Police said the babies' bodies were being gradually defrosted and that autopsies would begin on Tuesday.
No one in the family or in the neighborhood realized the woman, who is overweight, had been pregnant, Giese said.
The family were long-time residents of Wenden in what witnesses described as a well-tended half-timbered house in idyllic rural surroundings. Neighbors said the family was 'unremarkable' - friendly and settled into the neighborhood.
Series of child deaths
Germany has been plagued by a series of gruesome baby killings in recent years.
Most notable was Sabine Hilschenz, in eastern Germany, who killed nine of her newborn babies and hid the remains in buckets and flower pots as well as in an old fish tank at her parents' home.
The divorced, unemployed dental assistant told investigators she did not harm the children but left them to die after giving birth alone every time following heavy drinking. She was found guilty of eight counts of manslaughter in 2006 and is currently serving a 15 year prison sentence.
In December 2007 a 31-year-old woman was arrested after police recovered the bodies of five children aged between three and nine years old were found in a house in Darry, near the northern city of Kiel.
The same week a woman was arrested in Plauen in eastern Germany on suspicion of killing three of her own newborn babies. The bodies were discovered in a trunk in the cellar, on the balcony and in the fridge.
Last November, a 35-year-old woman from Erfurt was sentenced to 12 years in jail for killing two of her babies and hiding their bodies in a freezer.