He was with his mother when they became separated, a post on social media said.
In a statement, the family paid tribute to the "energetic, amusing and cheeky" boy and thanked everyone who helped them search for Julian after they appealed for help in finding him. We are so blessed to have had him in our lives and will remember... His family has our deepest sympathies at this very hard time.
The translated statement said: "The family of Julian Cadman has told us that unfortunately he is one of the victims of the attack and has asked us to thank all the people who have spread the news".
"Julian is 7 years old and was out with Jom when they were separated, due to the recent terrorist activity".
"We're urgently looking into reports of a child believed missing, who is a British dual national".
The group were plotting much deadlier carnage using explosives favoured by Islamic State militants, according to the Associated Press.
The van ploughed into crowds on Barcelona's Las Ramblas boulevard on Thursday afternoon, killing 13 people in the tourist hotspot.
The boy's father arrived in Barcelona from Australia on Saturday and, accompanied by psychologists and other emotional support professionals, went to the city's Institute of Legal Medicine to identify his son's mortal remains. A 14 person died in a second attack, six hours later, in the resort of Cambrils.
It comes as Catalan police issued a statement to quell widely-published false media reports that Julian had been "found alive" in a hospital in Barcelona.
The investigation is also focusing on a missing imam who police believe could have died in that house explosion.
Five terrorists were shot dead in Cambrils, including four apparently shot down by a single policewoman.
Some 34 nationalities were among those hurt in Las Ramblas and Cambrils, which lies around 70 miles to the south west.
Mr Bakkali said she appeared to be suffering two broken legs, a back injury and had a large wound on her head. Another two victims from Portugal, a woman and her grandmother, have not yet been publicly identified.
Earlier Friday, May spoke with Spanish Prime Minister Maiano Rajoy over the double terror attacks.