Angela Cannings went on trial in February
A jury of eight women and four men found Angela Cannings guilty on both counts, at Winchester Crown Court on Tuesday.
Cannings, 38, of Salisbury, had denied the murder charges and claimed both babies were victims of Sudden Infant Death Syndrome (SIDS).
Her first child, Gemma, died in 1989 at the age of 13 weeks but Cannings did not face charges in relation to her death.
Sentencing her, Mrs Justice Heather Hallett expressed regret at the mandatory life sentence: "It's not my decision to ask when you will be released but I intend to make it known in my remarks that in my own view you will never be a threat to anyone in the future".
"I have no doubt that for a woman like you to suffocate these babies there must have been something seriously wrong with you," she said.
'Exceedingly distressed'
Cannings broke down in tears as she was led away to the cells.
Her husband Terry, 48, who has stood by his wife since her arrest in 1999, was said to be distraught at the verdicts.
Her solicitor Bill Bache said his client was "exceedingly distressed - she cannot understand it".
Wiltshire Police said afterwards: "There are no winners in a case like this."
Cot deaths
Canning's three children were initially thought to be cot deaths victims.
However, police suspicions were aroused by the death of Matthew in 1999, and more detailed medical tests using advanced techniques were carried out.
Cannings was charged in March 2000 with the murder of all three infants, but the charge in relation to Gemma's death was later dropped.
After the verdict, Wiltshire Child Protection Unit announced a review into how cot deaths are investigated.
But parents' groups feared their reaction to cot deaths could lead to a witch hunt.
Joyce Epstein, of the Foundation for the Study of Infant Deaths, said: "The vast majority of these deaths are natural tragedies and to have unfair suspicion cast on parents who suffer this tragedy doesn't do anyone any good."