Relatives of Julian Cadman, a dual British-Australian national, appealed for information about his whereabouts after he became separated from his mother in the massacre on Las Ramblas that left 13 dead and at least 120 injured.
In a statement, released by the Department of Foreign Affairs and Trade in Australia, his family said: "Julian 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.
"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.
"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."
Julian's father and grandmother travelled to Spain from Australia following the attack, and his grandfather Tony Cadman had urged people to share a photograph of Julian on Facebook as fears for his safety grew.
In the photograph, Julian is wearing a jumper with a crest that says Chiddingstone Nursery, which is a nursery school in Kent.
On Saturday, the Philippines' government said a seven-year-old child missing following the attack is the son of a 43-year-old Filipino woman who had been living in Australia.
Foreign Affairs Undersecretary for Migrant Workers Affairs Sarah Arriola said the woman was with her son in Barcelona to attend the wedding of a cousin from the Philippines.
Ms Arriola said the woman, who was seriously injured, became separated from her child in the attack, and her British husband was heading to Barcelona to try to find his son.
Foreign Secretary Boris Johnson tweeted: "I send my sincerest sympathies to the family of Julian Cadman and all those who loved him. His death is a tragedy.
"The FCO, our Australian colleagues & the Spanish authorities continue to do all we can to support his family at this deeply distressing time."
A Foreign Office spokesman said: "We are assisting the family of an Australian-British child who was killed in the Barcelona terrorist attack.
"His family have our deepest sympathies at this very difficult time. Our staff are doing all they can to support them, working with our Australian colleagues and the Spanish authorities."