Jordan Burling's mother, Dawn Cranston, 45, was sentenced to four years in jail and his grandmother, Denise Cranston, 70, was handed three
His sister, Abigail Burling, 25, was jailed for 18 months.
The older pair were convicted on Tuesday of manslaughter after paramedics called to their home in the Farnley area of Leeds in June 2016 said Mr Burling resembled a victim of a Second World War death camp.
He was covered in bed sores and wearing a soiled nappy when he died from acute bronchopneumonia at his home in the Farnley area of Leeds in June 2016.
After a five-week trial at Leeds Crown Court Mr Burling's sister, Abigail Burling, 25, was cleared of manslaughter on Tuesday but found guilty of causing or allowing the death of a vulnerable person.
Before the trial, Dawn Cranston admitted trying to conceal a birth after hiding the remains of her dead baby in a rucksack for around 14 years.
The judge, Mr Justice Spencer, told the three women it was "almost beyond belief" that Jordan "should have been allowed to die in his own house, here in Leeds, in 2016, in the bosom of his family".
"It is important to emphasise that this was not a deprived household in material terms, nor were any of you inadequate to the point that you were unable to live a reasonably normal life outside the home," he added.
"Although the house was full of clutter you all had mobile phones, laptop or tablet computers and great deal of other equipment.
"The house was well-stocked with food. There were three refrigerators or freezers.
"Through your gross negligence, a precious human life was lost needlessly."
In a statement read outside court, the family of Mr Burling's father, Steven, said: "It has been truly horrific to learn in court the full extent of the pain and suffering that Jordan went through, and also to discover that Steven had another son who he and the family knew nothing about."
It said the family had been "denied the quality time we should have had with Jordan" and they felt "betrayed by the people we trusted to care for" him.
They will always remember him has "bubbly and chatty", they added.
"We have had two years of hell coming to terms with Jordan's death and we would like to thank the police and everyone involved who has helped to support us through this dreadful time.
"We now want to be left to grieve in peace and to lay Jordan and the baby to rest with the dignity and love they deserve."
During the trial, prosecutor Nicholas Lumley QC told jurors: "Jordan had been allowed to decay, to rot to death, by those closest to him, over a period of, at least, several weeks."
Dawn Cranston was even heard telling a 999 operator shortly before Mr Burling's death that his unresponsive state was a "blessing" as it meant she would not have to go work that day, the court heard.
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Several witnesses claimed that Mr Burling's mother "did not seem bothered" as medics attempted to revive him with CPR, while Denise Cranston supposedly remained seated in a nearby armchair.
James Rogers, chair of the Safer Leeds executive, said a full independent review being taken into Mr Burling's death.