Rishi Sunak said the "unprecedented package" - equivalent to 15% of GDP - could go further if demand is greater, and vowed to do "whatever it takes" to help the economy.
The Chancellor, speaking at a press conference inside 10 Downing Street, also said he was extending the business rates holiday to all businesses in the hospitality sector and funding grants of up to £25,000 for smaller businesses.
And Mr Sunak said that for those in financial difficulty due to coronavirus, mortgage lenders will offer a three-month mortgage holiday.
He unveiled the measures after the Government's chief scientific adviser said around 55,000 people in the UK now have Covid-19, as the NHS moved to cancel all non-emergency surgery and 71 people are now known to have died.
Sir Patrick Vallance told MPs it is hoped the death toll can be kept to under 20,000 as he told of the huge amount of strain the health service will be under from Covid-19.
Mr Sunak said: "This is not a time for ideology and orthodoxy, this is a time to be bold, a time for courage.
"I want to reassure every British citizen this Government will give you all the tools you need to get through this."
He said the Government would "stand behind businesses small and large", and announced an "unprecedented package of Government backed and guaranteed loans to support business to get through this".
"Today I am making available an initial £330 billion of guarantees, equivalent to 15% of our GDP.
"That means any business who needs access to cash to pay their rent, their salaries, suppliers or purchase stock will be able to access a Government backed loan or credit on attractive terms.
"And if demand is greater than the initial £330 billion I'm making available today, I will go further and provide as much capacity as required. I said whatever it takes, and I meant it."
Describing the outbreak as an "emergency", he added: "Never in peacetime have we faced an economic fight like this one."
Boris Johnson said the Government "must and will act with a profound sense of urgency" and would be like a "wartime government".
The Prime Minister also warned that Covid-19 is so "dangerous" that without drastic action it will "overwhelm the NHS", as he warned that more "extreme measures" may be needed to protect lives in the future.
Shortly before the press conference, NHS England chief executive, Sir Simon Stevens, told MPs the NHS would be "flat out" helping coronavirus patients for the next four to six months.
He has sent a letter to hospitals telling them to prepare for a big influx of patients requiring ventilation and ordered moves to cancel non-emergency surgery by April 15 at the latest, alongside the discharge of medically fit people to free up beds.
During a hearing of the Health Select Committee, chairman Jeremy Hunt asked Sir Patrick whether the expected death rate was one fatality for every 1,000 cases, which would mean that there are "potentially 55,000 cases" at present.
Sir Patrick said: "We've tried to get a handle on that in Sage (Scientific Advisory Group for Emergencies) and if you put all the modelling information together, that's a reasonable ballpark way of looking at it.
"It's not more accurate than that."
As well as the headline £330bn package of support for businesses and homeowners just announced by the Chancellor, the government says it is speaking to industry leaders and asking them for ideas about how to ease red tape and help them survive the coronavirus crisis.
As a result, pubs and restaurants in England will now be able to turn themselves into takeaway without changing their license - a potential lifeline in an age of social distancing. Licensing is devolved, so the Scottish Government would need to take similar action to affect businesses in Scotland