The Horgen court found the 39-year-old Swiss citizen of Austrian origin guilty of murdering the twins, a boy and a girl, and of manslaughter for the death of the other child, a baby boy, court spokeswoman Bea Rosenberger told AFP.
The woman was handed a life term, which in Switzerland usually amounts to around 15 years behind bars, and ordered to undergo psychiatric therapy while in prison.
The woman, identified only as Bianca B. by Swiss media, had for years insisted she was not responsible for the twins' deaths in late 2007, but suddenly changed her story in a tearful confession during her trial last month.
She told the court she had murdered them both and also admitted to smothering her first child, a seven-month-old boy believed until then to have died from sudden infant death syndrome in 1999.
"I wanted him to be quiet for a while," she was quoted as saying by the ATS news agency.
Despite maintaining her innocence for a long time, Bianca B. was sentenced to life in prison for the twins' deaths in an earlier trial in March 2010, but she was granted a retrial after the court determined her defence had been flawed.
She has been in jail since the end of 2007 awaiting a final verdict, and the five years already spent behind bars will be deducted from her sentence, Rosenberger said.
At the opening of her new trial on December 12, Bianca B. described in detail how on the evening of December 23, 2007, she had gone into her son's room after placing the children's Christmas gifts under the tree and had suddenly, without thinking, picked up a pillow and pressed it against his face "until he stopped moving."
She had then gone into her daughter's room and done the same to her, before realizing what she had done.
"I didn't want this," she told the court, in tears.