Ashley Clarke, aged 24 and Scott Cain, aged 23, were both found unconscious in the apple store at Lord Selborne's Blackmoor Estate, near Liss on Monday (February 17).
Paramedics had tried to resuscitate the two men.
Post-mortem tests were inconclusive. The cause of death is unknown but nitrogen is used in the storeroom to preserve the fruit but a cause of death is unknown, the coroner’s office said.
Toxicology tests are being conducted.
Colleagues raised the alarm when the pair failed to return from work in the store.
‘Tragic work-related incident’
A police spokesman said: "These deaths are being treated as unexplained and the full circumstances of this tragic work-related incident are being investigated by the police with the assistance of the Health and Safety Executive."
Inquests into the deaths are due openned today (February 22) by the North Hampshire coroner.
Viscount Wolmer, Lord Selborne’s son and md of the 1,000ha estate, said in a statement: "Two members of staff at Blackmoor packhouse were found unconscious in an apple store on the afternoon of Monday 18 February.
“Despite the efforts of staff and the emergency services, they were subsequently found to have died.
“This is absolutely devastating news for our tight-knit community and our thoughts are with their loved ones.
“The cause of this tragic incident is being investigated and Blackmoor Estate is co-operating fully with the authorities.”
Clarke’s father said in a statement: “He had a passion for life and the utter devastation felt by everybody who knew him is testament to his popularity and the impact he had on many of those who knew and loved him.
"We still have many questions which will need to be answered in the fullness of time, but nothing will bring Ashley back or take away the incredible pain we are all feeling.”
Cain was from Liphook and Clarke was Liss in the north east of the county.
Twitter tributes followed the deaths. Gary Tarbuck tweeted: “In shock tonight. RIP Ashley Clarke. Thoughts with friends and family at this very sad time #tooyoung.”