The infant is likely to have permanent brain damage as a result of a sickening attack by Taylor Biggins.
A court heard how the baby was found unresponsive when police went to a flat in the early hours of October 25 last year.
Leeds Crown Court heard the baby was in a critical condition after suffering skull fractures and bleeding to the brain.
Doctors feared the victim would not survive the injuries which they assessed as being non-accidental and consistent with being shaken
Biggins was arrested by police the following day and denied any wrong-doing.
He initially claimed he had found the baby unconscious and not breathing when he went to check on him.
The 24-year-old later changed his account, claiming the baby suffered the injuries after accidentally falling to the floor.
Biggins admitted inflicting grievous bodily harm shortly before he was due to go on trial.
The court heard Biggins pleaded guilty to the offence on the basis that he did not intend to cause serious injury.
Biggins, of Middlegate, Birstall, stated he had acted in temper when the baby would not settle after waking in the early hours of the morning.
The defendant also stated in his basis of plea: "I accept that I picked him up and shook him and threw him across the bed.
"He went across the bed and struck his head on the TV cabinet.
"I accept by my actions that I am responsible for the totality of the injuries."
Biggins has a previous conviction for assault, dating back to 2015, when he kicked a former partner in the stomach while she was pregnant.
Tom Storey, prosecuting, said a police investigation revealed Biggins had gambling problems.
He had lost money in the hours leading up to the incident on live football betting which may have contributed to his bad temper.
Mr Storey said medical experts expect the baby to have "at least mild cognitive impairment to his motor skills in the years to come."
The prosecutor said it is too early to assess the full extent of the injuries due to the victim's age.
The baby also suffered damage to his retinas but it is not yet clear whether his eye sight has been permanently damaged.
A victim statement was read to the court on behalf of the baby's mother.
She described Biggins' actions as a "poisonous act".
She said: "(The baby) is likely to have brain damage throughout his life
"The sad reality is that no prison sentence will compare to the life sentence he has caused."
Adrian Waterman, mitigating, said: "No one suggests that he intentionally set out to hurt (the baby) that night.
"It seems clear that it was his own failings, his own inadequacies, his own immaturity, which he allowed to get the better of him.
"This was a moment of utter madness born out of his own failings and immaturity and lack of responsibility."
Judge Rodney Jameson QC jailed Biggins for two years and ten months