The cap will come into effect for around 24 million households in Scotland, England and Wales on default energy tariffs on October 1, and will remain in place until December 31, when it will be adjusted again.
The 4.5 million pre-payment meter customers, who are often the most vulnerable and already in fuel poverty, will see an even more punishing increase, with their average annual bill set to go up to £3,608.
Ofgem's chief executive Jonathan Brearley warned of the hardship energy prices will cause this winter and urged the incoming Prime Minister and new Cabinet "to provide an additional and urgent response to continued surging energy prices".
The regulator said the increase reflected the continued rise in global wholesale gas prices, which began to surge as the world unlocked from the Covid pandemic, and had been driven still higher to record levels by Russia slowly switching off gas supplies to Europe.
Mr Brearley said: "We know the massive impact this price cap increase will have on households across Britain and the difficult decisions consumers will now have to make. I talk to customers regularly and I know that today's news will be very worrying for many.
"The price of energy has reached record levels driven by an aggressive economic act by the Russian state. They have slowly and deliberately turned off the gas supplies to Europe causing harm to our households, businesses and wider economy. Ofgem has no choice but to reflect these cost increases in the price cap.
"The Government support package is delivering help right now, but it's clear the new Prime Minister will need to act further to tackle the impact of the price rises that are coming in October and next year.
"We are working with ministers, consumer groups and industry on a set of options for the incoming Prime Minister that will require urgent action. The response will need to match the scale of the crisis we have before us. With the right support in place and with regulator, Government, industry and consumers working together, we can find a way through this."
Fuel poverty charities immediately called on the Government to urgently extend the household support package announced in May - when the price cap was predicted to reach around £2,800 in October - "to prevent the bleakest of winters".
Adam Scorer, chief executive of fuel poverty charity National Energy Action, said: "The scale of harm caused by these price rises needs to sink in. A warm home this winter will be pipedream for millions as they are priced out of a decent and healthy quality of life.
"Households need money in their pockets to weather this storm or we are going to see millions in dangerously cold homes, suffering in misery with unimaginable debt and ill health.
"Action is needed now to prevent the bleakest of winters."
Simon Francis, co-ordinator of the End Fuel Poverty Coalition, said: "Today's Ofgem price hike is like a dagger to the heart of millions of people up and down the country.
"As a result of the decision, parents will be unable to feed their children, the sick and elderly will be condemned to worsening health, disabled people will go without vital medical equipment and households will be forced into poverty for the first time in generations.
"All the solutions lie at the Westminster Government's door, yet it is silent in the face of this looming disaster."
Philippe Commaret, the managing director of energy giant EDF, has warned that half of UK households could be in fuel poverty in January as a result of rocketing prices, while Which? has urged the Government to raise its energy bills discount by at least 150% or risk pushing millions of people into financial distress.
The consumer watchdog said the Government's financial support for all households must increase from the current £400 to £1,000 - or from £67 to £167 per month from October to March.
However, no immediate extra help will be announced by Boris Johnson's Government, with major financial decisions being postponed until either Liz Truss or Rishi Sunak is in No 10 after the Tory leadership contest.
On Wednesday, Chancellor Nadhim Zahawi insisted "nothing is off the table" when it comes energy bills, but added that a freeze in the price cap would not deliver "targeted help" for those who need it most.
Based on Wednesday's gas prices, experts at consultancy Auxilione think the cap will reach £5,210 in January 2023 and £6,823 in April.