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.

The Saracens winger, 28, was cited for making contact with the eyes of Ulster's Luke Marshall in a European Champions Cup game.
The suspension came just a week after he was recalled to the England squad, 18 months after his last appearance.
Ashton pleaded not guilty at a hearing on 20 January and is appealing against the level of the sanction.
He received the full written decision of the independent disciplinary hearing judicial officer on Friday, 22 January.
England begin their Six Nations campaign in Scotland on 6 February and end it on 19 March in France, with Ashton's ban finishing on 28 March.
Head coach Eddie Jones said he would wait for the outcome of any appeal before naming a replacement.
However, Bath wing Semesa Rokoduguni has been called up as cover and the 28-year-old will join up with the England squad until a final decision is made on Ashton's case.

The alleged victim, now in his 40s, was under 16 when he was at Grafton Close Children's Home, during the 1980s.
The man told the jury at Southwark Crown Court how Father Anthony McSweeney performed a sex act on him and then took out a camera.
Fr McSweeney, 68, of Pease Pottage, West Sussex, denies abusing boys at the home in Hounslow, west London.
The priest, of Old Brighton Road North, denies four counts of indecent assault, three counts of making indecent images of a child and one of taking indecent images of a child.
The alleged victim told the court the incident took place in a flat at Grafton Close belonging to John Stingemore.
The jury has been told that he abused boys during his time as the home's manager. He was due to be tried alongside Fr McSweeney but was found dead in his home last month.
When the alleged victim was asked why he did not tell anyone at the time what had happened, he replied: "Who would I tell? There was no-one else other than the staff.
"It would only get reported to Mr Stingemore.
"I felt a bit ashamed as well."
The alleged victim also described how the priest fondled him over his clothes as he sat on his lap while playing video games, and offered to help him wash as he was having a bath.
During cross-examination, Stephen Spence, defending Fr McSweeney, put it to the man that he was not telling the truth, which he denied.
The trial, which is expected to last two weeks, was adjourned until Wednesday.
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.
[NEXT_CONCEPT]
Chris Ashton will appeal against a 10-week ban that would rule him out of England's entire Six Nations campaign.
[NEXT_CONCEPT]
A Roman Catholic priest took photographs of a boy after sexually abusing him, a jury has been told.