Hayley Davidson died in hospital after being found at a house in Buckhaven, Fife, on 14 February 2016.
Gordon McKay, 38, had originally been charged with the infant’s murder but at the High Court in Livingston he pleaded guilty to the lesser charge of culpable homicide.
McKay, who had been left to look after her, will be sentenced next month.
The 38-year-old, who lived a few doors along the road from Hayley and her mother, said he had found the baby cold to the touch on a beanbag in his living room.
He told police he then shook her three or four times in an effort to revive her.
Three days later, Hayley Davidson died from a head injury at the Royal Hospital for Sick Children in Edinburgh.