The sons were both given suspended prison sentences.
Some of the information was used in Hutcheson's legal case against Ramsay, after the chef accused his father-in-law of embezzling over £1m.
Gordon Ramsay's father-in-law has started a six-month prison sentence for computer hacking as part of a bitter feud with the firebrand celebrity chef which has lasted the best part of a decade.
The court heard that during one day in February 2011 Hutcheson accessed the computer system 600 times, while Adam accessed it 282 times.
Christopher Hutcheson, 68, and his sons Adam, 46, and Christopher, 37, admitted plotting to unlawfully access Gordon Ramsay Holdings Limited's system.
Some of the information the Hutchesons obtained ended up in newspapers, including a revelation that the chef had had a hair transplant.
In 2011, Ramsay's lawyers won a High Court ruling allowing Hutcheson Senior's computer to be searched over the hack.More news: Here is the list of Apple devices that will get iOS 11
When news of the hacking broke, Hutcheson Sr emailed his son Chris, saying, "Guess we have been rumbled".
Prosecutor Julian Christopher said that the two families had already reconciled and did not support criminal prosecution, the Guardian reported.
Hutcheson Snr, who has a home in Druillat, France, gave an address of Wycombe Place, Earlsfield, south-west London, while Hutcheson Jnr is from Welwyn Garden City, Hertfordshire, and Hutcheson is from Sevenoaks, in Kent.
They were sentenced at the same court on Wednesday, June 7.
It was alleged the accounts were hacked to access material that could prove useful in civil litigation proceedings between Ramsay and Hutcheson Snr.
He said items including photos were "provided to the press which led to considerable intrusion into the privacy of the family".
The judge said that despite the seven-figure impact of the civil legal battle between the older man and his son-in-law, only immediate imprisonment was appropriate given the seriousness of his crime.