The Australian boy is among the 13 people killed when a van ploughed into crowds in the Spanish city.
His seriously-injured mother Jumarie, or Jom, remains in hospital, one of more than 100 people hurt in the attack that has been claimed by Islamic State.
Julian had been missing since the van was driven through a pedestrian walkway in the busy Las Ramblas district on Thursday but authorities have now confirmed the boy with dual Australian-British nationality died.
The seven-year-old was much loved and adored, his family said.
“As he was enjoying the sights of Barcelona with his mother, Julian was sadly taken from us,” the Cadman family said in a statement on Monday.
“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.”
Julian and his mum were in Barcelona for a weekend family wedding.
The boy’s father Andrew arrived in Barcelona from Sydney on Saturday evening, not knowing his son’s fate.
Family members in Australia and England had posted appeals on social media to find Julian.
The Cadman family thanked those who helped search for Julian and said their thoughts and prayers were with all people affected by the attack.
The community at Julian’s Sydney school, St Bernadette’s Catholic Primary in Lalor Park, are feeling his loss deeply, said Catholic Education Diocese of Parramatta executive director Greg Whitby.
“Julian was a delightful little boy – curious and energetic with a kind and generous heart,” Mr Whitby said in a statement on Monday.
“He was much loved by his teachers and fellow students.”
A team of counsellors are at the school.
Foreign Minister Julie Bishop said the Australian government was deeply saddened to confirm Julian’s death.
Spanish police and authorities tweeted in Spanish that Julian had been formally identified, while Spain’s Interior Ministry said his identity had been confirmed by DNA testing.
British Foreign Secretary Boris Johnson tweeted his sympathies to Julian’s family and all those who loved him.
“His death is a tragedy,” Johnson said.
“The FCO (Foreign and Commonwealth Office), our Australian colleagues & the Spanish authorities continue to do all we can to support his family at this deeply distressing time.”
Federal Opposition Leader Bill Shorten and Shadow Foreign Minister Penny Wong described Julian’s death as every parent’s nightmare.
“The sadness of Julian’s death is matched only by the evil of those who took his life,” they said.
The Cadman family has asked to grieve in private.
Sydney woman Suria Intan, who was on the last few days of a European holiday with friends, was also seriously injured in the attack.
Intan is a Commonwealth Bank worker who is heavily involved with Hillsong Church. A spokesperson told AAP its church in Barcelona is supporting her and her family.
Four Australians were injured in the attack including two Victorian men who were hit by the van.
The men, named in media reports as friends Robert Bogdanovski and Anthony Colombini, were released from hospital soon after the incident.
Local News Matters
Media diversity is under threat in Australia – nowhere more so than in South Australia. The state needs more than one voice to guide it forward and you can help with a donation of any size to InDaily. Your contribution goes directly to helping our journalists uncover the facts. Please click below to help InDaily continue to uncover the facts.