The coke ovens and blast furnace at the Redcar steelworks will close after no offers to buy them were received, the Insolvency Service has confirmed.
The ovens had been kept alight until the weekend to allow for negotiations with prospective buyers.
But official receiver Ken Beasley said there was no "realistic prospect" of a sale and he could no longer spend taxpayer money to keep the plant going.
Local MPs have said the loss of 2,200 jobs is devastating.
The works has been hands in the hands of receivers since the site's owner Sahaviriya Steel Industries UK (SSI) was wound up on 2 October.
'No realistic buyer'
The closure of the coke ovens and blast furnace means the end of steel production at the 98-year-old Redcar works.
Once the furnace and ovens are closed it would take months and millions of pounds to get them going again, as happened when SSI re-opened the works in 2012.
Mr Beasley, said: "I cannot continue to draw on taxpayers' funds to keep the ovens operational when there is no realistic prospect that a buyer will be found.
"I am continuing my liquidation of the company, including talking with interested parties about purchasing the company's other assets."
'Towel thrown in'
Anna Turley, Labour MP for Redcar, said she was angered by the decision to close the works.
She told BBC Tees: "I can't believe all this has been allowed to go, all the history and heritage and potential for the site.
"I feel the government has thrown the towel in. I feel the official receiver was never interested in talking to anyone or listening to any deals, or any other options to keep it going."
She said she would call for an inquiry: "I cannot believe the government has allowed 170 years of steelmaking to fade away with no fight, no determination and no understanding of what this means to our area, to people's livelihoods and to the British economy."
Tom Blenkinsop, Labour MP for Middlesbrough South and East Cleveland, said it was a dark day for the area and accused the government of "abandoning Teesside".
He said: "This is devastating news for the 2,200 workers who have lost their jobs."
Middlesbrough MP Andy Macdonald, also Labour, said the closure was "industrial vandalism".
Business Secretary Sajid Javid said the closure was "disappointing" but the government was unable to intervene in the liquidation process.
He said the government would provide up to £80m to "support people who have lost their jobs as a result of SSI's liquidation, and mitigate the impacts on the local economy".
Mr Javid also said the government would host a steel summit on 16 October to "explore" the challenges the UK steel industry is facing.
Business Minister Anna Soubry said: "I had hoped that a commercial buyer for the coke ovens could be found, but unfortunately this has not happened.
"This news is very, very disappointing and my thoughts are with the workers and their families."
SSI blamed a global slump in the value of steel for its original decision to mothball the Redcar works last month.