Julian and his mother Jom had been in Barcelona for a family wedding, and became separated when a van ploughed into crowds in the city's busy Las Ramblas district on Thursday evening (local time).
The Department of Foreign Affairs and Trade released a statement on behalf of the Cadman family saying he was "a much loved and adored member of our family".
"As he was enjoying the sights of Barcelona with his mother, Julian was sadly taken from us.
"We are so blessed to have had him in our lives and will remember his smiles and hold his memory dear to our hearts."
The family thanked those who had helped in the search for Julian and said their thoughts and prayers were with the families of other victims in the Barcelona attack.
They asked for privacy and said they would not be making any further statements.
Foreign Minister Julie Bishop said in a statement she was "deeply saddened" to confirm Julian Cadman's death.
A statement from St Bernadette’s Catholic Primary Lalor Park, the school that Julian Cadman attended said "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."
"The Diocese of Parramatta stands ready to provide the family and the St Bernadette’s community with any assistance needed. Counsellors will be at the school this week, and for as long as they are needed, to support students and staff" the statement said.
In a Tweet, Boris Johnson, UK Secretary of State for Foreign and Commonwealth Affairs, extended his "sincerest sympathies to the family of Julian Cadman and all those who loved him".
"The FCO [Foreign & Commonwealth Office], our Australian colleagues & the Spanish authorities continue to do all we can to support his family at this deeply distressing time."
Julian's mother remains in hospital, one of more than 100 people hurt in the attack that has been claimed by Islamic State.
The Daily Mail has reported she underwent surgery, while Fairfax quoted a hospital official saying her condition was "less serious" on Saturday.
As news of the terror in Barcelona spread, extended family, both in Australia and the UK, posted appeals on social media to find Julian, who the Australian government reported as missing.
Julian's father, Andrew, arrived in Barcelona from Australia on Saturday evening to try and find his son, who is a British-Australian dual national.
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.
The UK Foreign Office had also been providing assistance to the Cadman family.
Another Sydney woman, Suria Intan, who was on the last few days of a European holiday with friends, is also in a serious condition in hospital after being injured in the attack.
Ms 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 have been released from hospital.
They have been named in media reports as friends Robert Bogdanovski and Anthony Colombini.