Brothers Dennis and Bernard McGinley from Taunton, Somerset, and Christy Stokes from Micheldever, Hampshire, threatened to shoot the victim, who cannot be identified for legal reasons.
Teesside Crown Court heard he was forced to empty his bank account, borrow money and sell his tractor.
The men were jailed after pleading guilty at an earlier hearing.
Dennis McGinley, 40, was jailed for seven years and four months. Bernard McGinley, 35, received a sentence of four and a half years, and Stokes, 44, was jailed for three years and nine months.
The court heard the conspiracy began in August last year when the gang visited the victim's North Yorkshire farm.
Over a period of 17 days they forced him to hand over £196,000, by saying a mini-digger he had bought previously had been used for a "drugs run", and they had information which could put him in jail.
He was forced to drop off cash at car parks across the country.
At one drop-off the farmer was told he was "going to get a bullet in his head" and at another he was warned his "entire family" would be killed, Glenn Parsons, prosecuting, said.
The victim finally went to the police when his money ran out.
Sentencing, Judge Simon Bourne-Arton said to the men: "Such was your greed, such was your complete disregard for the effect upon this family, that no sooner had one payment been made that another demand was made, so money was handed over the same day or following days."
In a victim statement read out in court, the farmer said his family was "terrified".
"My wife locked my daughter in a cupboard, we were that scared these people were going to come and get us if we didn't pay any money," he said.
The gang has now paid back the £196,000, the court was told.
Three men who blackmailed a North Yorkshire farmer, forcing him to pay them almost £200,000, have been jailed.