Harry Whitlam died after Gary Green, 51, of Bradburn Road, Wakefield, reversed the vehicle into him at Swithens Farm, Rothwell, near Leeds, in August 2013.
Leeds Crown Court heard he was more than two times the legal driving limit.
The court was told Green must have consumed the equivalent of 13 pints of beer before going to bed at 02:00 BST.
Harry's mother Pam Whitlam, who worked at the farm's cafe, said her close-knit family had been "changed forever".
"It is not OK for anyone, whether on a public road or private land, to be drunk and get behind the wheel of a vehicle," she said.
"My hope today, now the court process is complete, is that Harry's life becomes more than one day and as a family we can again remember the good times we shared."
"We all miss him dearly and it has not got easier with time but harder," she added.
"Harry was my youngest son, a much-loved brother, grandson, nephew and cousin.
"The only memories I currently have of Harry are from the day of the accident but his life was so much more."
Green, who was jailed for 16 months and two weeks, had previously admitted failing to ensure the safety of others.
He was prosecuted under health and safety legislation rather than road traffic law as he was on private land at the time of Harry's death.
During an investigation by the Health and Safety Executive (HSE), inspectors found he had been walking towards a worker in a closed-off area of the farm when Green backed the tractor into him at about 09:15 on 9 August.
HSE inspector Julian Franklin said it was "an extremely tragic case" and described Green's behaviour as "reckless".
A drunken tractor driver who knocked down and killed an 11-year-old boy has been jailed for more than a year.