Twenty others were also affected after a hot tub on display at JTF warehouse in Stoke-on-Trent exposed people to harmful levels of Legionella bacteria.
Richard Griffin, Harry Cadman, 71, from Stoke-on-Trent and William Hammersley, 79, Chesterton died in 2012.
JTF will be sentenced at Stafford Crown Court on Monday.
It admitted failing to ensure the safety of employees and customers under the Health and Safety at Work Act.
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Not guilty verdicts on two corporate manslaughter charges were accept by the judge at Stafford Crown Court and three other health and safety charges were allowed to lie on file.
A report by the Health Protection Agency (HPA) in 2012 said the hot tub was the probable source of the "significant" outbreak.
In 2015, it emerged that more than £200,000 has been awarded to families after the deaths.
Mr Griffin, 64, contracted the disease while delivering meat to a café in the warehouse in Fenton.
He initially suffered headaches and hallucinations and later lost consciousness at his home in Clayton. He died in hospital from multiple organ failure.
His family said he had never taken a day off sick in 30 years.
A firm has admitted a health and safety breach after an outbreak of Legionnaires' disease in a hot tub caused the deaths of three men.