“The family would like to thank everybody for their extraordinary support,” the statement said.
It added that they were deeply moved by the many messages they have received from across Ireland and around the world.
They said they had been touched “by the wonderful portrayals” of their “beautiful son and brother, Stephen”.
They also confirmed his funeral will take place on Saturday in a church just yards from where the 33-year-old grew up and went to school.
“The family would like to confirm that their son and brother, Stephen, is returning to Ireland on Friday with a funeral service in St Laurence O'Toole's, which is taking place on Saturday at midday.”
They also emphasised that they never doubted that Stephen's death had been caused by anything other than natural causes.
His mother Margaret, when hearing of the results of the post-mortem, said that she believed that her son died from the same heart condition that has plagued the family in the past.
The heart condition comes from his father's side of the family, and it is suspected it may have played a part in Stephen's death.
The singer was found dead on a sofa in his apartment in Majorca on Saturday afternoon. Stephen became ill while he slept following a night out with his husband, Andrew Cowles (32), and a friend of the couple, who returned to their apartment with them.
Spokesman Gerald Kean also repeated yesterday that the couple's friend, Giorgio Dochev, stayed in the spare room of their apartment on Saturday night.
Following Tuesday's autopsy, preliminary tests indicated that Stephen had smoked cannabis but further tests are needed to confirm this.
Toxicology tests are expected back within a fortnight. It is not illegal to smoke cannabis in your private home under Spanish law. Selling and growing the drug is against the law.
“The family reiterate their position that they never had any doubts that Stephen died as a result of natural causes,” they added.
“The family are still trying to come to terms with the tragic loss and would like people to respect their privacy,” they added.
Preparations for the funeral service — expected to draw a crowd of thousands to the Sherriff Street church in Dublin's north inner city — continued yesterday, with Boyzone involved heavily in its planning.
Boyzone also released a statement in which they said that their “brother” was now resting in a chapel in Majorca.
“Stephen's body was released by Spanish authorities following an autopsy that confirmed that Stephen had died from natural causes,” it read. The band also thanked everyone who had sent messages of condolence.
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? firstname.lastname@example.org