Demolition work began last Wednesday at the Dunfield Terrace site, which was partially destroyed in a fire in the summer of 2022.
Derry City and Strabane District Council previously order the site owners to demolish it.
Dunfield Residents’ Association spokeswoman Felicity McCall said people living in the area were delighted that the action was now finally being taken.
She told BBC Radio Foyle’s North West Today programme: “The most positive benefit is that no longer can it be a haven for antisocial behaviour that had become such a big issue.
“Perhaps the authorities will realise this is not a suitable site for development on so many counts.”
Building work stopped at the Dunfield site more than four years ago.
Residents have long held concerns about antisocial behaviour in the area and have previously held a series of protests at the site.
In November 2022 Derry City and Strabane District Council ordered the owners of the site to remove the structures and hoardings.SDLP Waterside councillor and chair of the council’s Planning Committee Sean Mooney said he was delighted work was now progressing.
He added that there was an onus on the council to take the views of local residents into consideration should any future planning applications be submitted for the site.