The 37-year-old mother, named by Spanish newspapers as Sara Lopez Hernandez, "denied killing the babies", her lawyer Manuel Caballero told news agency AFP.
A court in the southern city of Seville handed her a 35-year jail term, he said, after a jury had found her guilty on September 17th.
The court also ordered her to pay €300,000 ($384,000) in compensation to her ex-husband and her three living children.
Lopez went on trial after her husband found the babies in freezers in their home near Seville in 2012. Autopsies showed they had died by suffocation.
State prosecutors had demanded a 40-year jail term, branding her "a monster of a mother".
The mother reportedly told the court she had given birth to one of the babies alone in the bath, having kept the pregnancy secret from her husband.
The local newspaper Diario de Sevilla quoted Lopez as telling the court she had not killed the babies and that she "adored" them.
She said one of the babies was stillborn and she had kept the body in the freezer so as "not to be separated" from the child.