"Spy Booth", depicting men "snooping" on a telephone box, appeared on a private house in Hewlett Road in April.
On Wednesday, Q Scaffolding erected wooden panels around it, prompting fears from locals it would be removed.
Now John Joyce, of Q, has said the homeowner was paid for the work, which will be auctioned and he expected could fetch up to £1m.
Mr Joyce said part of the work would be removed "on Friday", and part of it "on Sunday or Monday", before being taken to London for the sale on 4 July.
He explained the landlord of the property had sold the piece for an undisclosed amount.
"We are not doing anything illegal. We are preserving Banksy's legacy," he said,
He added that by removing the artwork it would protect it and "stop it being vandalised".
Earlier, Cheltenham Borough Council said it believed the owner of the house had arranged for scaffolding to be erected in order to repair rendering on the wall.
People living nearby guarded the site overnight to ensure the work was not removed.
A spokesman for Gloucestershire Police said there was an increased presence of officers in the area because of "social tension" that has developed among residents who do not want to see it go.
Cheltenham's Liberal Democrat MP Martin Horwood earlier said he would be "disappointed" if the owner of the house decided to sell the work.
At the beginning of June, Banksy admitted painting it - three miles away from the government listening post, GCHQ.
Since then "Spy Booth" has attracted hordes of visitors.
A Banksy artwork in Cheltenham will be removed, the company that erected scaffolding around it has confirmed.