Angelika and Marcin Klis had not been seen since the explosion at the Ariana Grande concert on Monday night.
The couple's daughter Alex Klis, 20, a student at York College, had posted an appeal on Facebook for information about their whereabouts.
The Polish foreign ministry confirmed two Polish nationals had been killed.
It is understood Mr Marcin, 42, worked at York Cars Taxi Service, a cab company in York.
Mr Marcin and his wife, aged 39, had taken a picture of themselves together in Manchester shortly before going to the concert to collect their daughters.
This was shared on social media by their daughter on Tuesday.
She wrote: "Anyone who is in any safe place or hospital in Manchester, if anyone comes across my parents please please let me know as they've been missing ever since the attack, this is a picture taken tonight so this is exactly what they were wearing."
In a statement, the Polish foreign ministry said: "We share the pain of the family and the loved ones of the victims and express our most sincere condolences.
"Consuls have offered assistance to the family of the victims."
The Polish Foreign Minister, Witold Waszczykowski, told a radio station: "The parents came after the concert to collect their daughters and unfortunately we have information that they are dead. The children are safe."
Dr Alison Birkinshaw, principal at York College, described the deaths as "devastating news for Alex and her family, the whole college and the wider community".
She said: "We are in touch with Alex and will do whatever we can to support her and her family."
A JustGiving page has been set up to raise money for Ms Klis and her sister Patrycia and has so far raised more than Â£4,000.

TPG Capital and the Ontario Teachers' Pension Plan want to buy parts of Fairfax Media including its newspapers and property advertising arm, Domain.
A deal could be worth as much as A$2.5bn (Â£1.4bn).
However, loss-making Fairfax said the offer "may not optimise shareholder value".
It also said the proposal may not get off the ground "given the complexity involved in splitting the businesses".
A deal would also need approval from the federal government's Foreign Investment Review Board.
Fairfax, which also publishes The Age and the Australian Financial Review, posted a loss of A$893m last year as it struggled with plunging print advertising revenue and newspaper sales.
Last week journalists at the Sydney Morning Herald and The Age in Melbourne went on strike for a week in protest after management announced more job cuts.
However, the Domain division, which accounts for half of Fairfax's profits, is growing strongly and the company wants to spin it off and retain a majority stake.
Domain is Australia's second-biggest real estate website after one owned by Rupert Murdoch and is valued by analysts at about A$2bn.
According to Fairfax, the consortium has offered 95 cents a share for Domain, along with the metropolitan newspapers, an events business, and a start-up investing arm.
That would leave existing Fairfax shareholders with assets including newspapers in regional Australia and New Zealand, as well as stakes in the Macquarie Radio Network and Stan, a video-streaming service.
Shareholders would also be left with existing debt.
Lee Mickelburough, of Henderson Global Investors, which owns about 5% of Fairfax shares, said: "It's a troublesome structure to say that we get 95 cents for the good business and you get to keep the debt for the transition businesses. It's cheeky, the way they've structured it."
Shares in Fairfax gained 2.4% in Sydney on Monday following news of the bid, valuing the company at about A$2.5bn.
A Polish couple living in York who had gone to Manchester Arena to pick up their daughters have been killed in the terror attack.
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The owner of Australian newspapers including the Sydney Morning Herald is in takeover talks with a North American private equity consortium.