Letby, 34, was found guilty last August of murdering seven babies and trying to kill six more between June 2015 and June 2016 while working as a nurse in the neonatal unit of the Countess of Chester Hospital in Chester, northern England.
She was jailed for life and told she would never be released.
Letby denied having harmed any baby in her care.
Last month, she went on trial for a second time on one count of attempted murder of a further baby girl, known as Child K, a charge on which the original jury had failed to reach a verdict.
Prosecutor Nick Johnson told Manchester Crown Court that Child K was born prematurely at 25 weeks in February 2016 at the hospital, and had been connected to a ventilator and other machines monitoring her heart rate and oxygen levels.
Little more than an hour after the birth, while other staff were absent, Johnson said, senior doctor Ravi Jayaram entered the room where she was being looked after to find the baby's breathing tube dislodged, alarms that should have sounded had become disabled, and Letby standing there "doing nothing".
Johnson added that on two further occasions that night, Letby interfered with the breathing tube to give the impression there was a particular problem with the baby.
"Justice has been served and a nurse who should have been caring for our daughter has been found guilty of harming her," the family of Child K said in a statement read outside court by police.
"But this justice will not take away the extreme hurt, anger and distress that we have all had to experience."
"These were the actions of a cold-blooded, calculated killer," Senior Crown Prosecutor Nicola Wyn Williams said in a statement on Tuesday following the verdict.
Child K died in a different hospital three days later, although the prosecution said this had nothing to do with the allegation against Letby.
In her evidence, Letby again denied having ever harmed any baby put in her care, and said she had no recollection of the night in question.
Her defence lawyer said the evidence was not there to prove her guilt.
Letby was originally found guilty of killing the five baby boys and two baby girls by injecting the infants with insulin or air, or force-feeding them milk.
The case shocked the UK and prompted the government to order an inquiry into why concerns about her behaviour had not been heeded by hospital bosses.
Police also said they were carrying out further investigations into whether there were other victims at hospitals where Letby had previously worked.
For some on social media, Letby has become a cause celebre who was herself a victim of a terrible miscarriage of justice and, ahead of the latest trial, the New Yorker magazine ran an article questioning the evidence against her.
In May, however, England's Court of Appeal rejected her attempt to overturn her conviction, which had been mainly based on arguments that evidence from the prosecution's expert witness was flawed.
Letby had also argued jurors were wrongly told they did not have to be sure how she was alleged to have killed or attempted to kill her victims.
But Judge Victoria Sharp said in a ruling made public on Tuesday, that "it was not necessary for the prosecution to prove the precise manner in which she had acted".
