PepsiCo said in March it was consulting about plans to close the Peterlee factory to help it make "productivity and efficiency savings" in the UK.
A spokeswoman confirmed earlier that production would be moved to the company's other UK sites by December.
She said 355 workers had been given notice earlier and all those affected would be offered support.
The company is still consulting with its subsidiary firm PRDC Transport about the fate of 23 additional posts associated with the crisp factory.
Tracey Foster, Peterlee manufacturing director at PepsiCo UK said: "We appreciate that this is very difficult news for everyone at the Peterlee site.
"We would like to emphasise that this decision in no way reflects the performance of our colleagues at Peterlee and we remain very grateful for their hard work and commitment.
"Efficiency savings are crucial for ensuring the long-term sustainable growth of our business in the UK."
At the time of the consultation, the Labour MP Grahame Morris said the closure proposal was a "bitter blow" for East Durham.
In a statement released earlier, the Easington Labour prospective parliamentary candidate said: "PepsiCo has confirmed it has decided to proceed with the closure of the Walkers manufacturing site at Peterlee by the end of December 2017."
Some of the famous crisps made at the factory include Walkers, Lays, Sensations, Scampi Fries, Bacon Fries, Cheese Moments and Cheetos Twisted, the firm said.
1960: The factory opened as Tudor Crisps
1961:  It was bought by Smith's Crisps
1989: Walkers bought the factory from Smith's Crisps
2017: The factory is due to close

The scrum-half was allowed to return to the field after belatedly being sent for a head injury assessment.
The group said Murray "did not meet the criteria for immediate and permanent removal from the field of play".
Munster were not fond to have broken concussion management protocols.
Ireland's Murray said he did not lose consciousness in the European Champions Cup game at Scotstoun on 14 January.
In a statement on Wednesday, the EPCR Untoward Incident Review Group summarised its decision.
"In the 62nd minute of the match, Murray went to ground following a tackle on an opposition player and was attended to by the Munster medical team. Following an on-pitch assessment, the player resumed play.
"After real-time video footage of the incident was reviewed by the Munster medical team pitchside, the player was then temporarily removed from the field as part of the HIA process for further assessment, before subsequently returning.
"After studying footage and documents submitted by Munster Rugby, the Review Group was satisfied, on the balance of probabilities, that Murray did not meet the criteria for immediate and permanent removal from the field of play.
"The Review Group concluded that Munster's medical team and more specifically, their Team Doctor, followed the World Rugby Head Injury Assessment (HIA) protocol and used the MyPlayXPlay real-time video system that the club had invested in, to review the initial on-field assessment of the injury."
Sale Sharks were cleared of wrongdoing by the Concussion Management Review Group (CMRG) for an incident involving back-row forward TJ Ioane in a Premiership game in January.
However, Northampton were found to have breached rules by allowing Wales winger George North to play on after a head injury a month earlier.

The man was found unconscious at a flat in Caledonia Court on Wednesday.
He was treated at the scene and taken to Galloway Community Hospital where he was pronounced dead a short time later.
Police Scotland said there were no apparent suspicious circumstances and the procurator fiscal had been informed.
More than 350 jobs in County Durham will be axed when Walkers crisp factory closes, the owner has confirmed.
[NEXT_CONCEPT]
Munster have been exonerated by the European Professional Club Rugby (EPCR) over their management of a head injury sustained by Conor Murray against Glasgow in January.
[NEXT_CONCEPT]
Police are investigating the unexplained death of a 32-year-old man in Stranraer.