Mr King said plans for spending cuts worth £6bn in 2010 were "sensible".
Investors also gave a cautious welcome to the new government - with UK bond prices rising, although sterling weakened.
Meanwhile, earlier Conservative plans to scrap the Financial Services Authority have been shelved.
Mervyn King took the unusual step of praising the new government's plans at the Bank's quarterly Inflation Report media conference.
The Liberal Democrats may have swallowed some extra spending cuts, but the Conservatives have taken on a lot of Lib Dem tax policies in return
Stephanie Flanders
BBC economics editor
Read Stephanie's blog
The coalition: Business speaks
He said the measures planned by the Conservatives and agreed by the Liberal Democrats demonstrated a commitment to cutting the deficit.
He also implied that the previous Chancellor Alistair Darling had not gone far enough with his Budget policies.
Mr King warned that recent events in the eurozone had shown how quickly markets could turn against a country which was seen to lack credible plans to cut borrowing.
FSA saved
In a published agreement between the Conservatives and Liberal Democrats, the two parties committed themselves to a "significantly accelerated reduction" in the budget deficit over the course of the next parliament.
A plan for deficit reduction will be set out in an emergency budget within 50 days, with £6bn in cuts to "non-front line services" to be made in the 2010-11 financial year.
Spending plans will be based on independent growth and borrowing forecasts, the agreement said, rather than Treasury forecasts.
The City regulator, the Financial Services Authority (FSA), is also set to remain, despite earlier Conservative plans to scrap it.
The new Business Secretary Vince Cable
, who will also oversee banking reform, said that although the regulator would continue to operate, the Bank of England
would have overall responsibility for the stability of the banking sector. The FSA has previously been criticised for its supervision of banks in the lead up to the financial crisis.
Other financial measures in the agreement include:
•A full spending review, to report by the autumn, to decide where cuts in spending will come
•Establishing an independent commission to review the long-term affordability of public sector pensions
•Reductions to Child Trust Fund and tax credits for higher earners
•A "substantial increase" in personal allowance for income tax from April 2011, with a longer-term objective of increasing the personal allowance to £10,000
•Lib Dem plans for a "mansion tax" on properties costing more than £2m dropped
•Conservative plans to raise the inheritance tax threshold to £1m dropped
•The introduction of a banking levy, and measures to tackle "unacceptable" banker bonuses
•An independent commission to look at banking reform, including the possibility of breaking up the banks into retail banks and investment banks
Market reaction
POUND STERLING V US DOLLAR
Last updated: 12 May 2010, 23:06 UK
*Chart shows local time
More data on this currency pair The rise in the price of UK government bonds - known as gilts - showed some confidence in the ability of the coalition to make inroads into the public-sector deficit, BBC business editor Robert Peston
said. He added that the gap between the yield on equivalent German and UK government bonds had narrowed, "which shows that investors believe the risk of lending to the British government has reduced".
Sterling had rallied briefly after the formation of the new coalition government, but the gains were short-lived as concerns over the fragile economic recovery took hold.
Having breached the $1.50 dollar mark early in the session, the pound fell sharply after the Bank of England predicted inflation would remain low - even if interest rates stayed at record lows.
The pound also reversed earlier gains against the euro, with one pound worth 1.175 euros.
On the stock markets - where movements in recent days have been heavily influenced by attempts to solve the eurozone debt crisis - the FTSE 100 index fell in early trading, but then recovered to close up 0.9% at 5383.5 points.
Business leaders welcomed the new government's focus on the budget deficit.
"Business wants to see a stable government with the authority to take the tough decisions that will be required to keep the economic recovery on track and to get a grip on the fiscal deficit," said Richard Lambert, director general of the CBI.
The new regime will be fairer, with benefits for low earners, but it could strip the rich of their favourite tax shelter
Anne Redston
Professor of Tax Law Kings College, London
How will the new coalition policies affect your finances?
The British Chambers of Commerce joined the CBI in calling for the deficit to be the main priority.
"Fixing the public finances must be at the top of the agenda. The Conservative-led coalition must be absolutely clear about where spending cuts will fall," said David Frost, director general of the British Chambers of Commerce.
The Institute of Directors (IoD) also called for a smaller public sector.
"The key test facing the coalition is whether it can maintain a stable government over a significant period of time that delivers large cuts to public spending, and whether it can generate policies across all areas that genuinely supports business and economic growth," said the IoD's director general, Miles Templeman.
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