The land is earmarked for the enhancement of the town's outdoor market - and Marston's Estates expect the works to take up to 6 weeks to complete.
The Market Street pub, which was built in the early 1970s, is on land owned by the council and Marston's Estates has agreed to surrender its long term lease.
The pub sits adjacent to other land in the council's ownership and will provide the opportunity to enhance links with the bus station and the metro, and potentially create development land at the same time.
The outdoor market will continue to operate during the demolition works.
The proposal forms part of the wider regeneration of Bilston.
Marston's Estates spokesperson said: "We were given the opportunity to work closely with the council surrounding the potential of the land that the pub was situated on. We believe that this is of benefit to Bilston and support the regeneration work of the city council."
Marston's recently invested in the area, developing and opening a family pub/restaurant, the White Rabbit, at Bilston Urban Village, following on the back of new homes being built and the area seeing extensive areas of open space landscaped for public use.
The first phases of works also produced significant investment in the building of the Bert Williams Leisure Centre and South Wolverhampton and Bilston Academy - improving health and increasing opportunities.
A commercial development plot fronting the Black Country Route and the newly named Bert Turner Boulevard linking the site with the town centre was also created.
Cabinet Member for City Economy, Councillor John Reynolds, said: "The demolition of the Hop Pole pub is another sign of progress in Bilston.
"It will enable the land to be better utilised for the benefit of the town and, in particular, the outdoor market.
"It is part of the wider regeneration of the area to deliver new homes, new jobs and more investment. It demonstrates our commitment to Bilston and ensures it will continue to be a thriving area."
Bilston was also announced in October as one of the pilot towns for the West Midlands Combined Authority (WMCA) town centre programme.
The programme will offer new funding, expertise and support from the WMCA and other partners, and will be delivered by councils.