All 330 workers at the site will lose their jobs over the next two years as the site is run down and finally closed early in 2017.
Management says the plant has become commercially uneconomic, hit by falling sales and the high cost of the pound on international markets.
Tyres are no longer made at the factory, which was the first opened by Akron, Ohio-based Goodyear outside of the USA in 1927, but it produces rubber compounds for tyre factories overseas as well as retread tyres.
But the raw materials for the compound mixing process are all imported, and the compounds are then exported to Goodyear plants abroad. The company says this is no longer financially viable, and in future the mixing process will take place at the tyre plants. The factory has 267 workers in the mixing department.
Another 53 work on producing retread tyres, but the company says it is too small to continue on the site on its own. Another 10 people work in support roles at the factory.
Generations of Wolverhampton people have worked at the plant, and the majority of the existing workforce is aged over 55.
"This is extremely disappointing news and we are seeking an urgent meeting with the company.
"While we recognise Goodyear is a global business that has to make global decisions, we would urge the company, which has a deep-rooted history with the city, to reconsider this decision.
"Should the worst happen, we will work with Goodyear to explore what support can be offered to those facing redundancy, and draw on the help and advice of trade unions and partners to provide new training opportunities.
The company says it will make every effort to find new jobs for those losing their jobs.
The news was broken to the workforce at a meeting this morning. Shortly beforehand management briefed representatives from the main union on the site, Unite, as well as local MP Emma Reynolds.
Emma Reynolds, MP for Wolverhampton North East, said: "Goodyear is an iconic Wolverhampton company. Generations of families have worked at the factory.
This proposal is a serious blow to all those who work at the factory, their families and our city.
I am demanding an urgent meeting with the company to establish exactly what their reasons are. My understanding is that the factory has high levels of productivity and is profitable.
Twitter reacts to news of the closure
I hope that there might still be a possibility that the company will reconsider its decision and I will be working with both the company's management and trade unions to find a way forward. I am also writing to the company's senior management to seek answers.
I am also calling an urgent meeting to discuss the potential closure with Wolverhampton City Council, the Local Enterprise Partnership and other significant employers and business people so that it the factory does close, we can help provide other opportunities in the local area to the workers."
Councillor Peter Bilson, deputy leader of Wolverhampton council, said: "We want to appeal to the management to reconsider their plans and to consider the implications to the workforce.
"Goodyear has been synonymous with Wolverhampton for generations.
"At one time we were their European headquarters.
"People will remember those times with great fondness.
"For now we need to do all we can to convince the company to keep a presence in Wolverhampton."
Under proposals laid out today, the first workers will leave under voluntary redundancy in October, but the plant will remain operating until early 2017 as its work is gradually transferred to other Goodyear sites across Europe and the Middle East.
Opened in the city in 1927, it was on its way to employing more than 6,500 people at its peak in the early 1980s, making tyres for cars, trucks, tractors and even Formula 1 racing teams. Covering 88 acres, the factory site stretched more than half a mile from one end to the other. along Stafford Road.
But cheaper foreign competition and a declining market has gradually eroded the factory, first with the loss of car tyre manufacturing
Following a deal with developer St Modwen the site was sold in 2002 and plans later drawn up that saw Goodyear shrink its operations to just 18 acres, with the entrance moved to Bushbury Lane and the rest of the site being turned into a new housing estate.
Goodyear has continued to invest in the plant, most recently unveiling a £6 million development in 2012, in the hope of turning around the factory's fortunes.
But today's decision brings manufacturing by Goodyear in the UK to an end. It's only other plant, making autosport tyres in Birmingham, closed last year after the site was bought by Jaguar Land Rover. Goodyear will retain a marketing, distribution and service operation at its TyreFort site at Erdington.