Toxicology tests are still believed to be ongoing, but police have previously said there were "no signs of suspicious circumstances" and the singer's family could be given permission to fly his body home today.
A lawyer for Mr Gately's family ruled out the possibility of suicide or the involvement of drugs.
Gerald Kean told GMTV: "This sort of thing does happen, we are absolutely happy that there is no foul play."
"[The family's] sole purpose and function at the moment is to try and get their son and brother home as quickly as possible."
Stephen Gately's grieving relatives have said they feel "vindicated" after the judge ruled the Boyzone singer died of natural causes.
The singer's mum, Margaret Gately, reportedly said: “As soon as I heard he had died I knew it was a heart problem."
Stephen’s father Martin has seen several relatives die prematurely from heart trouble.
The rest of the Gately family will have now medical checks to see if they too are at risk.
A man who was at Mr Gately's apartment the night he died has described finding the singer's lifeless body.
Georgi Dochev, 25, said he alerted Mr Gately's partner, Andrew Cowles, after finding him "very cold and white".
Bulgarian Mr Dochev is believed to have accompanied Gately and Mr Cowles back to the apartment in the resort of Port Andratx in the early hours of Saturday after a night out.
Mr Dochev has spoken to police who are investigating the death.
Members of Boyzone, Mr Gately's former band, returned home on Monday night after flying to the Spanish island on Sunday.
A spokesman said: "All the boys are home now. They went there to pay their respects and start dealing with the fallout of the situation.
"However, it's clear that them being there at the moment is bringing a lot more attention to the situation."
Ronan Keating, Keith Duffy, Mikey Graham and Shane Lynch met Mr Cowles yesterday at the Mon Port Hotel in the resort of Port Andratx, where they were staying.
The band said they were "completely devastated by the loss of our friend and brother, Stephen".
Mr Kean said Mr Gately had been in the apartment with Mr Cowles until after midnight on Friday, when he travelled to the town of Palma, about an hour's drive away.
He said a close family member spoke to Mr Gately at 12.30am Spanish time on Saturday (11.30pm British time) as he was getting ready to leave.
It is understood Mr Gately spent several hours socialising and was back in the apartment before 6am in Spain.
Mr Kean said: "We are not saying he was not drinking but eight hours is not something we accept."
He added that police had said they were not looking to speak to anyone else in connection with the death.
Mr Gately, who joined Boyzone in 1993 after answering an advert in Dublin to audition for Ireland's first boyband, shocked the pop music world 10 years ago when he announced he was gay.
He was introduced to Mr Cowles by Sir Elton John and his partner David Furnish and the pair married in a civil union in 2006.
LUNG CONDITION RARE IN YOUNG PEOPLE
Pulmonary oedema is rare in people as young as Stephen Gately and is normally associated with heart problems, according to Dr Joe Kidney, a respiratory adviser to the Northern Ireland Chest Heart and Stroke Association.
He said: “Pulmonary oedema is an accumulation of fluid on the lungs which you see in people with abnormal heart function.
"The commonest cause would be the heart not pumping properly. It is normally associated with fatal heart disease or heart attacks.”
Between 2001 and June 2009, 31 people in Northern Ireland died of pulmonary oedema.
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