They said they were “relieved” and “tired” as they left a Spanish prison and prepared to be reunited “as soon as possible” with their five-year-old son.
Brett and Naghmeh King were arrested on Saturday after they took Ashya from Southampton General Hospital without the consent of doctors last Thursday.
They walked free from Soto del Real prison near Madrid after British authorities dropped the case against them.
Mr King told reporters: “We’re very relieved to be free. We are very grateful to Spain for the support and help we have received. We will go to see my son as soon as possible – we have been dying to see his face for so long.
“Thank you to Spain for helping us and thank you to England too.” He added: “I’m sorry we can’t say more, I’m very tired.”
Announcing the news earlier in the day of his parents’ release, the five-year-old’s brother, Danny, said: “I’m in shock at the moment – we’ve been waiting so long for this moment to come, and it’s finally come.”
He thanked everyone who had supported their cause, including Prime Minister David Cameron and Deputy Prime Minister Nick Clegg.
The National Court in Madrid said in a statement that a judge had decided to free the couple after British authorities dropped the case against them.
The Crown Prosecution Service (CPS) had said it was seeking the withdrawal of the European arrest warrant that sparked the hunt for the couple. It said it had arranged with Southampton Magistrates Court for proceedings to be dropped.
Mr Cameron hailed the move, saying: “I welcome the prosecution against Ashya King’s parents being dropped. It’s important this little boy gets treatment and the love of his family.”
Simon Hayes, police and crime commissioner for Hampshire, said he would seek assurances about the “quality of the information” provided by Southampton General Hospital to police, which sparked the hunt.
He said: “In light of today’s announcement by the CPS, I now need to be assured as to the quality of the information given by Southampton General to Hampshire Constabulary.
“Now that Ashya is receiving the medical assistance he requires and Mr and Mrs King will be reunited with him, this is the time to analyse decisions that were made.”
A spokesman for University Hospital Southampton NHS trust said: “We are pleased that Ashya’s parents will be released and will be able to see their son.
“When Ashya went missing last week, we had no option but to call the police because we did not know where he was or what his parents’ intentions were.
“The police asked us to make statements about his clinical condition and need of medical care, and we stand by the accuracy of the information we gave.”
Patricia King, paternal grandmother of Ashya, said earlier yesterday: “He (brother Danny) is going to be allowed to see Ashya any time he wants. That will help a lot, because he’s got someone he loves with him. That is one thing, that he won’t be on his own.
“The way everybody has behaved – the hospital who are now backtracking, the police who are now backtracking – they’ve done wrong, they all know they’re wrong.”
Health Secretary Jeremy Hunt said the government was proposing to fly a top oncologist to Spain to advise the family. He said: “What we want to do is make sure that Ashya’s family get the best independent advice.
“We are arranging for an independent expert to fly, if the family would like, to Spain to give them advice as to exactly what the right course of action is for Ashya going forward.”
The family are said to have wanted Ashya to have proton beam therapy to treat his cancer.
Mr Hunt said the NHS offers the therapy for children who need it and had funded 99 patients in the last year, adding: “It is not always appropriate, it is not always safe.”
Brother Danny King said the family was hoping to get Ashya, who is being treated in Malaga, to Prague for proton therapy. “First, my parents have to get to see Ashya, and get the family together once again.”
An online petition calling for Ashya to be reunited with his parents had attracted nearly 200,000 signatures at 5pm yesterday.
Ethan Dallas, 16, a friend of Ashya’s brother, Naveed, who started the petition, delivered it to Downing Street yesterday and said the case had “touched the heart of nations”.
It also emerged that the family are planning legal action against Southampton General Hospital. Juan Isidro Fernandez Diaz, the couple’s lawyer in Spain, said they were “so sad”, adding: “They are going to prepare legal demands against the hospital in Southampton.”
The CPS said: “We have urgently reviewed the case and we consider there is insufficient evidence for a realistic prospect of conviction for any criminal offence. We have decided to stop the criminal proceedings.”
The hospital trust later made another statement giving the history of the case, saying that Ashya’s tumour was successfully removed on 24 July.
It added: “After surgery, a combination of radiotherapy and chemotherapy, in accordance with international protocols, is needed to prevent the tumour from returning. For best results, this treatment should start within four to six weeks of surgery. With such treatment, Ashya’s chances of survival are very good (between 70-80 per cent).
“During discussions, Ashya’s family indicated they wished him to undergo proton radiotherapy instead of standard radiotherapy. This option was explored with the family and they were informed that, in Ashya’s case, there is likely to be no difference in survival between standard radiotherapy and proton radiotherapy.”