Ashya's family said the Prague-based centre where he was treated had declared him cancer-free, The Sun newspaper reported.
"It has justified everything we have gone through because things are working out for Ashya," his father Brett King told The Sun.
The Kings sneaked Ashya out of Britain because they were told the proton therapy, which directs beams directly at a tumour and causes less damage to other organs, was not available under Britain's National Health Service.
"If we had left Ashya with the NHS we don't think he would have survived," Brett King said.
Ashya's mother Naghmeh said: "We have saved his life. It is a miracle we thought we would never see."
The Kings' decision to take their son away from a hospital in Southampton without doctors' consent led to their arrest in Spain.
They spent several days in police cells before their release and a High Court judge later approved their application to be allowed to take Ashya to Prague's Proton Therapy Centre for treatment.
"We were arrested for child cruelty and neglect," Brett King told The Sun. "But leaving Ashya in the NHS would have been far more cruel."
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