"Ignacio didn't survive the attacks," Ignacio Echeverria's sister Ana wrote on her Facebook page.
"My brother Ignacio tried to stop terrorists and lost his life trying to save others. Igna we love you and will never forget you," his other sister Isabel wrote on Facebook.
The Islamic State group claimed responsibility for the attack on Saturday by three assailants who mowed down people in a van before going on a stabbing spree in the Borough market area, killing eight people.
Friends of Echeverria, who lived in London, were quoted in Spanish media as saying that they were walking in the area when they saw what they thought was an ordinary fight.
On closer look, it appeared that a man was beating a woman.
Echeverria rushed over to help and tried to defend her with a skateboard he had with him, prompting British media to dub him the "skateboard hero."
He was last seen lying on the ground and had been missing since then.
Spanish Prime Minister Mariano Rajoy also confirmed that Echeverria, a 39-year-old HSBC expert in the fight against money-laundering, had died in Saturday's attack.
"We will always remember him for his heroic and exemplary act," he said on Twitter.
Rajoy later called for Echeverria to be given the silver cross of the Order of Civil Merit, which recognises "the extraordinary services of Spanish and foreign citizens for the good of the nation."
In a statement, Spain's foreign ministry said "his courage in defending a defenceless person helps remind us of the need to remain united in the face of the scourge of terrorism, faced with those who make violence and terror their only language."
But Spain has been unhappy at the sluggish pace of the British victim identification process, which led to an excruciating wait for Echeverria's two sisters, two brothers and parents.
Spain's Interior Minister Juan Ignacio Zoido called it "inhumane" for the family.
Echeverria's sister Ana also said the family had not yet been able to see the body.
"We want to see and be with Ignacio's body. It seems that we won't be able to be with his body until Friday at the earliest," she wrote on Facebook.
"We would like the British government to allow us to be with him...," she added.
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