The European Central Bank (ECB) will inject at least €1.1 trillion (£834bn) into the ailing eurozone economy.
The ECB will buy €60bn bonds each month from banks until the end of September 2016, or even longer, in what is called quantitative easing (QE).
QE in theory increases the supply of money, something that keeps interest rates low and encourages borrowing and therefore spending.
The news sent the euro to an 11-year low against the against the US dollar.
In late afternoon US trading the euro was down 2% at $1.1367. It also fell 1.1% against the pound to be worth 75.82, or €1.3187. It has lost 6% of its value so far this year.
Record low eurozone rates have failed to boost the 19-country euro area.
The ECB also said it would keep eurozone interest rates at 0.05%, a record low.
Rates have been at that level since September 2014.
ECB president Mario Draghi said the programme would begin in March.
Earlier this month, figures showed the eurozone was suffering deflation, creating the danger that growth would stall as businesses and consumers shut their wallets, as they waited for prices to fall.
Mr Draghi said the programme would be conducted "until we see a sustained adjustment in the path of inflation", which the ECB has pledged to maintain at close to 2%.
Shares rose in response to the news and bond yields, which are linked to the amount governments pay to borrow, fell, particularly those of the weakest countries including Italy, Spain and Portugal.
Lowering the cost of borrowing should encourage banks to lend and eurozone businesses and consumers to spend more.
It is a strategy that appears to have worked in the US, which undertook a huge programme of QE between 2008 and 2014.
The UK and Japan have also had sizeable bond-buying programmes.
But some economists question what impact, longer term, this move can have. "Economically it is irrelevant but at least markets have had fun selling the euro and buying bank equities and peripheral bonds," said Alastair Winter, chief economist at Daniel Stewart.
Mr Draghi said the ECB's own programme had been taken because it was necessary to "address heightened risks of too prolonged a period of low inflation".
Mr Draghi said there had been a "large majority" on the ECB's governing council in favour of triggering the bond-buying programme now - "so large that we did not need to take a vote".
Up until now, the ECB has resisted QE, although Mr Draghi reassured markets in July 2012 by saying he would be prepared to do whatever it took to maintain financial stability in the eurozone, nicknamed his "big bazooka" speech.
Since then, the case for quantitative easing has been growing.
In advance of the ECB's announcement, there had been speculation that the central bank would not actually buy any bonds itself, but would invite the central banks of eurozone member governments to do so.
Analysis: Nigel Cassidy, Europe business correspondent, Brussels
Arriving somewhat breathless for his news conference, thanks to broken lifts, Mr Draghi finally produced a QE package for Europe that received an initial thumbs-up from the financial markets. In cash terms, it was just slightly more than some were expecting - but not that much more.
On the question of sharing some of the risks of his bond-buying spree with the 19 national banks, Mr Draghi came out fighting, saying such arrangements were quite normal and starting to sound irritated when his questioners kept bringing it up. Yet for many, the eurozone is not a true monetary union if its liabilities are not shared equally.
It all showed that Germany's deep reservations about the dangers of printing money could not be overcome in Frankfurt. Yet once again, a European institution has reach an 11th hour compromise which will be considered and dissected by the markets over the next few days.
In the event, Mr Draghi said only 20% of the new asset purchases would require national central banks to shoulder risks outside their own borders.
But he added: "The modalities, the amounts, the rules, the limits that you just asked me about have been decided here in Frankfurt. So the governing council is the sole decision-maker and the decisions are meant to affect monetary and financial conditions across the whole euro area."
'Shock and awe'
The Italian Finance Minister, Pier Carlo Padoan, welcomed Mr Draghi's "ambitious strategy", which he said was "good for Europe".
Speaking in Davos to BBC economics editor Robert Peston, he said it would "push away any risk of deflation" and provide "an injection of confidence to markets".
But he added that it was "just one element" of efforts to restore the eurozone's economic fortunes. Structural reforms and further single market integration were also necessary, he said.
"Mario Draghi has been left with little choice than to begin a more robust than expected quantitative easing programme in a bid to awake the economies of the eurozone from their slumber," said Dennis de Jong, boss of trading site UFX.com.
"This play is seen by many as the last roll of the dice for the beleaguered euro. QE has had some success in the US and UK, but with such a patchwork of economies and banking systems in the eurozone, the jury is very much out."
Nancy Curtin, chief investment officer of Close Brothers Asset Management, said: "European QE is set to start with a bang rather than a whimper, a fact that will be well received by investors.
"However, the eurozone is far from out of the woods. Structural economic issues remain, and all eyes now turn to the Greek election, with concerns that the result may eventually lead to a default and exit from the monetary union - a move which could send shockwaves through investors in the eurozone."