Leeds City Council is to spend around £26,000 demolishing the boarded up former Wellington Stores in the middle of the Holdforth estate in New Wortley.
Police ordered the shop be closed down in July after it became a magnet for crime and disorder.
The closure order was instigated after a group of up to 30 people were involved in an incident in July where police officers and their vehicles were pelted with bricks and bottles.
An arson attack in October let the shop badly damaged.
Council chiefs say it would cost up to £30,000 to repair the council-owned building. The council’s director of environment and housing has approved the demolition, which is set to take place next month.
The YEP reported in October how residents were living in fear on the Holdforth estate, where firefighters had been attacked and council workers told not to visit alone for safety resaons.
Residents said a gang of up to 30 youths and men gathered on the estate most nights.
Community leader Bill Graham, of New Wortley Community Centre, said: “We welcome the fact that the shop will be demolished, but getting rid of the shop won’t stop then problems of anti-social behaviour.”
Mr Graham added: “It is an opportunity to look at what we might be able to do with that site as a community.”
A Leeds City Council report states: “Since the premises has become vacant following the closure order the council has spent £2,100 on security and maintenance for the premises.”