The supermarket giant has informed the council about its decision, and Wolverhampton South East MP Pat McFadden, and comes as it announced it would be shutting 43 stores around the country.
The store chain confirmed this morning that it had taken "a very difficult decision" not to proceed with the city dev elopement.
It said it would be working with Wolverhampton City Council to find alternative uses for the site as soon as possible.
It is one of 49 sites across the UK that Tesco will not proceed with.
"We understand that the news will be a real disappointment to many people in the local community. We are extremely grateful for the support we had received for the plans," Tesco spokesman James Wiggam said.
Councillor Roger Lawrence, leader of Wolverhampton City Council, said today: "We are extremely disappointed and angered by the decision of Tesco not to proceed with the Royal Hospital development, particularly given their long standing commitment to invest in the city.
"The council has done everything in its power to support Tesco to proceed with their plans, and I and senior council officers will now be seeking urgent discussion with Tesco about how to take forward the development of this key gateway site."
Mr McFadden said: "This decision is a betrayal of the people of Wolverhampton and a clear breach of the promise made to the people of the city. Less than a year ago, the UK managing director of Tesco gave a pledge on behalf of the company that this investment would go ahead in the coming financial year.
"Tesco has owned this site for 14 years. During that time it has remained undeveloped and a blight on All Saints and on the city more generally. The one useful thing they could do is to work constructively for a positive future use for the site.
"They have a duty to the people of the city whom they have let down very badly. But the proof of their future action can only be in what they do rather than what they say. Because after today, why would anyone believe what they promise about the future?"
Just two months ago bosses said they were still committed to building the long-awaited store at All Saints.
But it emerged last month they had placed the store under review.
The site has been a focus of frustration for the city, having been the subject of numerous delays since Tesco first unveiled plans for a new Wolverhampton store more than 10 years ago.
It was hoped the superstore would help regenerate one of the most deprived parts of the city.
The company has owned the site for 13 years and spent a decade in a bitter legal war with Sainsbury's over the right to build on land in Raglan Street, Chapel Ash.
The row was eventually settled in 2011 when both stores were given permission.
Sainsbury's opened its £60 million Chapel Ash store last year.
Tesco's chief executive Dave Lewis said: "It is with a heavy heart that I am today announcing that we are unable to proceed with 49 planned new store developments across the UK, including our planned store in Wolverhampton.
"Our performance as a business has fallen significantly short of where we would want it to be and my absolute imperative has to be to protect the future of our business for the circa 300,000 colleagues we employ in communities all over the UK.
"I know that this news will be a real disappointment to many people in the local community and we're extremely grateful for the support we've received for our plans. I am very aware of the importance of the site to the area and I am determined that we will work closely with the council to find the right solution for the local community."
Members of the community took to Twitter today to express their views on Tesco's decision: