One of Perth's longest-running property disputes has come to an end, with former socialites Radhika and Panjak Oswal agreeing to demolish their unfinished mansion in Peppermint Grove.

The couple purchased multiple blocks in the upmarket suburb in the early 2000s to build the home, dubbed the Taj on Swan.

It was believed they spent more than $25 million buying the land before starting construction of the home on the 6,600-square-metre site.

Work on the home ended in 2010 when the couple experienced business problems with their fertiliser plant in the Pilbara, and left Perth to set up in Dubai.

It was estimated they had spend close to $40 million on the unfinished home in the upscale suburb, which is home to some of Perth's wealthiest families.

Council relieved by demolition agreement

The abandoned construction is now covered in graffiti. ( ABC News: Stephanie Dalzell )

Peppermint Grove Shire President Rachel Thomas said the council was relieved the family had agreed not to continue a long-running fight to stop the home from being demolished.

She said council came to an agreement earlier this week that the Oswals would be given nine months to demolish the home.

"Under a consent order agreed to by both parties, the demolition or site works to demolish must start by December 31 and the full demolition must be completed by the 30th of September," she said.

"Now that's quite a long period of time. We'd prefer it to be quicker but that was her [Radhika Oswal's] request. We understand she wants to carry out the demolition in stages and salvage what she can."

Mrs Thomas said the unfinished building had been an eyesore and the council had been under pressure to resolve the issue.

She said she was relieved there had finally been a breakthrough.

"I'm very pleased with the outcome," she said.

"I think we all are. It has been a blight on the area and it's also been a source of anti-social behaviour in the area.

"It has been a disturbance for neighbours, so we are delighted that we've got a certain outcome now."

She said she understood from the Oswal's lawyer that the couple wanted to redevelop the site, which was capable of being turned back into six separate titles, but she also believed the site was the subject of a freeze order by the Australian Tax Office.