The Bradley Stoke tiler's mother Josephine and sister Gabriele also told an Athens court yesterday that the 35-year-old would continue to receive medical attention when he comes back, possibly as early as next week.
But relatives of Hogan's former wife Natasha Vasser, 36, who is now re-married and living in Australia with the couple's daughter Mia, have described the decision to allow him to be released from a psychiatric unit as "simply horrendous".
Hogan threw Liam and his sister 50ft from a fourth-floor hotel balcony in August 2006 after a row with his then wife during a family holiday to Crete. He then plunged to the ground himself.
Six-year-old Liam, who was a pupil at Wheatfield Primary School in Bradley Stoke, died of his injuries but Mia and her father survived.
Since the incident, Hogan has been incarcerated, first in jail and then in a psychiatric hospital after a Greek court ruled last year that he was temporarily insane when he killed Liam.
Witnesses at yesterday's court hearing said Hogan "jumped up with joy" and with tears in his eyes on hearing the decision to send him home "immediately".
He embraced his mother and sister, who have been staying at an apartment near the Athens hospital in order to visit him regularly.
They assured the court that Hogan would continue to receive medical attention in England "and all the love the family can give him".
Hogan was then rushed out of the court room and back to the Athens Psychiatric Hospital, where he has
been staying for the 16 months since he was acquitted of Liam's murder by another Greek court in January last year.
A court source said it would take "about a week" before Hogan would be able to board a plane for the UK, as the latest judgement has to be formally signed by all judges and other authorities, and then delivered to all parties concerned and to the British embassy.
Last night, Natasha's stepfather Brian Chandler told the Post: "The prospect of John Hogan returning after just 16 months of a recommended minimum of three years' detention in a psychiatric unit is simply horrendous.
"He will return, having pushed two children off a fourth-floor balcony, as a completely free man, with no conviction of any kind against him, and will therefore be free to travel the world, if he chooses, in search of Mia, the daughter he tried to kill."
Yesterday's hearing focussed on whether Hogan was fit to travel without endangering his own safety and that of other passengers and crew on the plane home.
The Crown Prosecution Service has already said that because Hogan was tried and cleared of murder in Greece, no charges will be brought against him in relation to his son's death in the UK.
But inquests into the deaths of British nationals abroad are routinely held and a second hearing into Liam's death is pending after a coroner's initial verdict of "unlawful killing" was overturned by the High Court after a challenge by Hogan's relatives.
Judges ruled Avon coroner Paul Forrest's verdict was undermined by a "serious error of law" and ordered a fresh hearing earlier this month.
Mr Chandler said: "We are totally dissatisfied with the Greek Court which reached a not guilty verdict (in a murder trial) in just one-and-a-half days, without calling a single eye witness, and without establishing the fact that John Hogan had pushed both children off the balcony.
"This was only revealed by the diligence of the Somerset and Avon Coroner, Paul Forrest, at the subsequent UK inquest. The Greek authorities had allowed the press speculation to persist that John Hogan had jumped 'with his children in his arms'.
"We are equally dissatisfied with the Crown Prosecution Service who, although they have the power to re-try John Hogan in the UK, have so far chosen not to."
Hogan's lawyer Kerstin Scheel, based at Withy King solicitors in Trowbridge, confirmed yesterday's ruling but refused to make any comment on behalf of her client.
During his trial, Hogan's legal team argued that he killed Liam in a "moment of madness" and in an interview with a national newspaper last year, Hogan said he was "psychologically ill", at the time of Liam's killing, not evil.
He made a number of suicide attempts in prison before his trial and had a family history of suicide, with two of his brothers having taken their own lives.