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.
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."