The Ministry of the Interior said Julian, an Australian and British dual national, had been identified through DNA.

The Cadman family released a statement through the Australian government, mourning the loss of their "funny and cheeky" boy.

"Julian was a much loved and adored member of our family," they said. 

"As he was enjoying the sights of Barcelona with his mother, Julian was sadly taken from us.  He was so energetic, funny and cheeky, always bringing a smile to our faces.  We are so blessed to have had him in our lives and will remember his smiles and hold his memory dear to our hearts.

Related: Father of missing Australian boy, 7, arrives in Barcelona as hopes fade

"We would like to thank all those who helped us in searching for Julian.  Your kindness was incredible during a difficult time.  We also acknowledge we are not the only family to be affected by the events, our prayers and thoughts are with all people affected.  

"We will not be making any further comments on this tragedy and ask everyone, especially the media, to give us the privacy we need to grieve away from the public eye."

The office of Foreign Minister Julie Bishop also released a statement.

"The Australian Government is deeply saddened to confirm that Julian Cadman, a seven year old Australian boy, was among those killed in the terrorist attack in Barcelona.

"We remain in close contact with the family who has requested privacy at this difficult and harrowing time and we ask the media to respect their request.

 "The Australian Government will continue to provide consular assistance to those caught up in the attacks and to their loved ones."

Greg Whitby, head of the Catholic Education Diocese of Parramatta, also paid tribute to Julian, who was a student at St Bernadette's Catholic Primary in Lalor Park.

"Julian was a delightful little boy – curious and energetic with a kind and generous heart. He was much loved by his teachers and fellow students. The school community is feeling his loss deeply," Mr Whitby said.

"Together with the St Bernadette's community, we pray for Julian's family, particularly his mother Jumarie who was seriously injured in the attack, his father Andrew, and for all those affected by this terrible event. Julian, you will be in our hearts always."

Mrs Cadman is still being treated for injuries sustained in Thursday night's terror attack on Barcelona's Las Ramblas boulevard, where a van driving at high speed mowed down more than 100 people, killing 13. Another person was killed in a second attack in Cambrils, 120 kilometres south-west of Barcelona, the following morning. 

Mrs Cadman's condition was described by a hospital official on Saturday as "less serious".

Another Australian woman, Suria Intan, remains in "special care" at a Barcelona hospital, a hospital spokeswoman told Fairfax, being treated for serious injuries from the terror attack.

Ms Intan is a Commonwealth Bank worker who is heavily involved with Hillsong church. A said its church in Barcelona was supporting her and her family.

Foreign Minister Julie Bishop had earlier confirmed four Australians were injured in the attack, including two Victorian men who have been released from hospital.

They have been named in media reports as friends Robert Bogdanovski and Anthony Colombini.

Julian's father Andrew Cadman had flown from Sydney on Friday night on a desperate mission to find his son, who at the time was reported by the Australian government as "missing" after Thursday's terror attack.

The family appealed for information through social media.

But an hour before Mr Cadman touched down in Barcelona, Spanish police issued a statement that suggested tragedy awaited him.

"Neither we were searching nor we have found any lost child in the Barcelona attack. All the victims and injured have been located."

Mr Cadman was met by Australian consular officials at Barcelona airport on Saturday afternoon, local time, and driven directly to the Ciutat de la Justicia.

According to a Catalan government statement, the Ciutat de la Justicia is where victims of the Las Ramblas terror attack are being identified by forensic experts.

Mr Cadman was then taken, with police car escort, to the hospital to see his wife.

The Daily Mail reported that five relatives and friends of Mrs Cadman were at her bedside at the Vall d'Hebron hospital, where she had undergone surgery and was now receiving care in a surgery recovery unit.

A Vall d'Hebron hospital spokesman said he had been asked by the family and by British and Australian consular officials not to talk to the media about the family's situation, beyond confirming a woman remained in a "menos grave" medical condition, which translates as "less serious".

Fairfax Media understands Mr Cadman was offered the option of spending Saturday night at the hospital, which was also offering him trauma counselling.

The UK Foreign Office has also been providing assistance to the Cadman family, with British Foreign Secretary Boris Johnson tweeting his condolences.

Mrs Cadman and Julian had been visiting Barcelona for a wedding when they were caught up in the deadly terror attack. Mr Cadman had stayed behind in Australia.