A number of options to display the artwork have been considered by the authority in recent years, including building a replica bridge on the original location.
Councillor Rob Pritchard, the portfolio holder for culture and leisure at Hull City Council said the chosen market location would help to improve access and security.
He said: “It will protect it from graffiti, damage or even from being stolen and allow people to see it in a safe space. It’s about finding a balance.
“It will also be protected from the weather so it should be a really good place to have it.”
The segment of bridge, measuring 22ft by 6ft (7m by 2m) and weighing more than a tonne, depicts a child wielding a wooden sword with a pencil attached to the end and a caption that reads: “Draw the raised bridge!”
Within days of its appearance in 2018, the artwork was defaced, which led to a protective screen being installed by the council.
Despite being one of the world’s most famous artists, the identity of Banksy remains unknown.
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