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Jacob Marx, 27, was walking on Camden Rd, north London, on Monday evening (UK time) when the metal hoarding from betting shop William Hill fell in strong winds and crashed on top of him, causing severe head injuries.
He reportedly suffered a cardiac arrest and was treated at the scene but died later in University College Hospital, the Daily Mail reported.
In statement, David Marx remembered his youngest brother as "a wonderful person, a special part of our family, and a much loved friend and partner".
"Losing him so quickly and so far away is very hard for us to come to terms with. We thank everyone for the love and kind support we've received as we try to grapple with what has happened," he said.
The Marx family thanked the emergency services and people in Camden who tried to help save Mr Marx.
"It means a lot to us that despite him being so far from home, people did their best to look after him."
The family are making arrangements to have his body returned to New Zealand.
Others who knew Mr Marx have paid tributes to the Gisborne man, described as likeable and clever.
Tim Chung, the brother of Mr Marx's girlfriend Natalie, said he "was really, really nice guy".
"He was really smart and I always saw him as a really nice person."
Mr Marx and Ms Chung travelled to the UK last September for a trip of a lifetime, said Mr Chung.
On February 2, New Zealanders taking part in the Waitangi Day Circle Line Pub Crawl in London will stop for a minute's silence at 10.05am to remember him.
At the scene of the accident, a written tribute has been left addressed to 'Jacko' and includes a New Zealand flag, the Daily Mail reported.
Left among bouquets of flowers, it said: "This is not how it was supposed to go. We had so many good plans and so many good memories. I promise never to forget you."
Witnesses who saw the accident said they saw a man covered in blood lying on the road, and paramedics attempted to resuscitate him in the ambulance as he was rushed to hospital.
The sign that fell on him may have been weakened after maintenance carried out before Christmas, media reports said.
Police and Camden Council are investigating.
Camden Council community safety spokesman councillor Abdul Hai said: "This is a tragic incident and our thoughts are with the victim's family at this sad time."