John Dobbie fractured the child's skull and left him blind and brain damaged after shaking him and striking his head.
Dobbie, 36, had denied attempting to murder the three-month-old boy at his home in Kirkcaldy, in Fife, in 2011 but was found guilty of the offence by a jury at the High Court in Edinburgh.
He was convicted of assaulting the baby to his severe injury, permanent impairment and to the danger of his life.
But they acquitted him of an earlier attack on the baby, who cannot be identified for legal reasons.
The child now suffers from cerebral palsy. He will never be independently mobile.
Dobbie arrived at the Victoria Hospital, in Kirkcaldy, with the child on June 5 in 2011.
Detective Constable Kim Stuart said Dingwall-born Dobbie had told him he had earlier fed the baby and changed his nappy and did not notice any marks on his body. Jobless Dobbie said he had needed to go to the toilet and put the child in an upright position but when he returned found he had slipped onto his side. He said he was shoogling the child.
He noticed the baby's eyes were rolling back. He took the baby to its mother and she told him to phone a taxi and take him to hospital.
But jurors heard expert evidence pointed to the baby suffering violent shaking and direct impact to his head. The judge deferred sentence on Dobbie for the preparation of a background report. Lord Armstrong said: "As you have heard the jury have found guilty of this grave charge."
Dobbie, who has been on bail up until now, was remanded in custody.