The Prime Minister, who polls suggest faces an uphill struggle to cling on to power, will promise to publish a blueprint to "really get Britain moving again".
In a webcast for the Downing Street website, he will set out an optimistic assessment of the country's prospects for economic recovery in the next 12 months.
But, echoing recent attacks on the Tories as elitist, he will warn against "a decade of austerity and unfairness where the majority lose out while the privileged few protect themselves".
Only Labour policies would ensure "the people on middle and modest incomes who don't want any special favours" benefited as well, he will say - according to extracts released in advance.
The message puts economic recovery at the top of a list of resolutions for 2010 that also includes "radical" public service reform, "a new cleaned up politics" and tackling terrorism.
And it includes a promise to publish later this week the first part of a "prosperity plan for a successful, fairer and more responsible Britain" - including investment in high-speed rail, aerospace, the digital economy, clean energy and other "industries and jobs of the future".
Mr Brown has faced some criticism from within his own ministerial ranks for what is perceived as a bid to launch a "class war" battle with Eton-educated David Cameron's Conservative Opposition.
But his New Year message will include a direct appeal to the party's core vote.
"There are some who say we must plan for a decade of austerity and unfairness where the majority lose out while the privileged few protect themselves," he will say.
"I believe we can create a decade of shared prosperity - with opportunities fairly shared among all those who work hard and play by the rules."
In an upbeat assessment, he will go on: "We can be incredibly proud that Britain's dynamic entrepreneurs have defied the recession to start up nearly half a million new businesses.
"There are now three million British businesses - more than at any point since records began in the 1980s, and fewer businesses closed in 2009, than in 2008.
"And I am confident that, if we continue with the tough decisions we have made, unemployment will start to drop this year, and more small businesses will open and flourish.
"That wasn't inevitable; it was the change we chose. And so my message today is simple: don't wreck the recovery.
"The recovery is still fragile, and it needs to be nurtured in the interests of those who were hit hardest by the recession - the people on middle and modest incomes who don't want any special favours - they simply want a bit of help to own their own home, set up their own business, and give their children the best start in life".
As the election looms - it must be held by June - the Prime Minister will declare that he believes the vast majority of British people believe things "have to" change.
"In my life, I have learnt that there are only really two kinds of people: those who think things can never change; and those who believe they have to.
"And I think the vast majority of British people are in the second camp. We are a nation that combines responsibility with fairness, compassion with aspiration - always reaching higher, dreaming bigger, aiming for ever greater things".
He will conclude: "My first priority is securing the recovery while cutting the deficit in a sensible and fair way.
"The second is radical reform of our public services while protecting frontline spending on schools, hospitals and the police.
"The third is a new, cleaned up politics.
"And the fourth is maintaining Britain's global strength and fulfilling our responsibilities against the terrorist threat from Afghanistan and the wider world.
"Britain is too great a country with so much potential - and people with such high aspirations - that in the coming decade we must not settle for anything less than big ambitions.
"We are determined to reduce the deficit at a responsible pace, without choking off the recovery or damaging the frontline services the mainstream majority rely on.
"And so our strategy is to go for growth, because we want to build our country up not talk Britain down.
"Later this week we will be publishing the first part of our prosperity plan for a successful, fairer and more responsible Britain: a plan detailing how we will invest in the industries and jobs of the future. From high-speed rail to aerospace to the digital economy to clean energy to advanced manufacturing, 2010 is when we will really get Britain moving forward again."
Shadow home secretary Chris Grayling said: "This backward-looking New Year message shows that despite warnings from his own Cabinet Gordon Brown remains intent on waging a negative and pointless class war.
"Gordon Brown has spent money like there is no tomorrow yet the gap between rich and poor has grown wider than ever. This message sounds like the last throw of the dice from a Government that has no idea how to solve Britain's problems."
Cabinet Office Minister Tessa Jowell warned Mr Brown last week not to turn the general election campaign into a "hideous" class war with Mr Cameron.
Her warning came after Mr Brown used a recent Prime Minister's Questions to accuse the Tory leader of pursuing policies dreamt up "on the playing fields of Eton".
The move was seen by some observers as a retreat into a "core vote" strategy appealing to Labour's traditional supporters rather than the broad alliance which backed Tony Blair to three election victories.
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