Events company Sincura Group, which controversially removed another Banksy mural in Tottenham, said it would exhibit the work before selling it for about Â£500,000.
Director Tony Baxter said the mural on a printing shop in Great Eastern Street would be removed by Sunday.
"It's a very iconic piece," he added.
A man who works in the printing shop said in 12 years he had not seen the Banksy mural because it has been covered with boards.
"I've seen pictures of what this building was like with it on about 15 years ago. Everybody's curious," he said.
Mr Baxter said the mural had become damaged with paint peeling away and would be restored before it was sold.
An image of Girl and Balloon painted onto the cardboard backing of an Ikea frame sold for Â£73,250 in 2012.
Last week, a developer expected to buy a block of offices from Camden Council was told it must remove a Banksy stencil of a rat and return it to the authority before the sale.
In the last year, two London Banksy murals have been removed from buildings - an image of a boy hunched over a sewing machine in Wood Green and another showing two children playing with a "no ball games" sign in Tottenham.
A spokesman for Banksy declined to comment.
A famed stencil image of a girl with a balloon by graffiti artist Banksy is being removed from the wall of an east London shop and sold.