The judge at the trial of father-of-two John Hogan described him as being "incapable" of murdering his son.
John Hogan leapt from a fourth floor hotel balcony
Court President Paraskeri Kiraleou ordered instead that the 33-year-old should be detained in a psychiatric unit "for therapy".
Mr Hogan threw his son Liam and daughter Mia from the fourth floor of their Crete hotel in August 2006.
The verdict follows evidence that Mr Hogan had suffered clinical depression since childhood.
The hearing was told that Mr Hogan, from Bradley Stoke, near Bristol, had stopped taking anti-depressants seven months before leaping from the balcony.
At the trial, he said he had been "mentally disorientated" when he grabbed Liam, six, and Mia, two.
Natasha Hogan gave evidence for the prosecution
Liam died from his injuries, but Mia survived.
The court was told that Mr Hogan's two brothers, Stephen and Paul, had both killed themselves.
And the accused had tried at least four times to kill himself.
The family, including his wife Natasha, was in Crete for a "make or break" effort to resolve differences in their marriage.
The court was told their home had been turned into "a little hospital" where "despair and grief ruled" following the onset of his father's ultimately terminal multiple sclerosis.
Mrs Hogan told the court her husband had worked hard to care for his family but since the birth of their children he had become increasingly depressed and unhelpful.
She said he confronted her about his fear that she was thinking of leaving him after he had tried to kiss her and she had moved away.
On the day of the incident she said her husband had become increasingly angry and agitated.
An official working for Hogan's lawyer, Dimitris Xiritakis, said of Mr Hogan: "He has suffered depression throughout his life It's such a tragic incident.
"We know he has tried to take his own life. This has been well documented."
John Hogan said he wanted to be with his son in heaven
Judges at the trial wanted to know why Mr Hogan had tried to kill himself in prison four times.
Mr Hogan told the court he wanted to die and go to heaven so he could be with his son, to be there to protect him.
Dr Jim Bolton, a consultant psychiatrist, said it was recognised that "severe depression can lead to thoughts that it would be better to be dead".
A statement on behalf of Mr Hogan said: "I have suffered from a mental illness for many years, perhaps from birth.
"My brothers, Stephen and Paul, committed suicide because of serious personality disorders."
He went on to say that he "felt lonely after the death of my father".
His older brother, Paul, had been a manic depressive who had been sectioned in hospital on a number of occasions.
In 2004, after setting fire to the family home, he committed suicide by jumping from Clifton Suspension Bridge, Bristol.
Mr Hogan's lawyers had argued he was not mentally fit to stand trial after a series of suicide attempts and should be held in a psychiatric unit.
But a series of psychiatric assessments in Athens, in November, found he was fit to stand trial.
Mind, the mental health charity in England and Wales, said one in four people will experience a mental health problem at some point during their life.
The support group said every year more than 250,000 people were admitted to psychiatric hospitals and more than 4,000 people took their own lives.