The ECB will also expand its quantitative easing program from €60 billion to €80 billion a month.
The bank also decided to further cut its bank deposit rate, from minus 0.3% to minus 0.4%.
The measures, including the decision to cut the main interest rate, were more radical than investors had expected.
The stimulus measures announced three months ago have largely failed to drive economic growth higher or boost inflation.
ECB president Mario Draghi told a news conference in Frankfurt that it had cut eurozone inflation projections to reflect the recent decline in oil prices.
The bank now expected inflation to be just 0.1% this year – substantially lower than the previous estimate of 1% and underlining the need for the bank to go further than expected.
Inflation should rise to 1.3% in 2017 and 1.6% the following year, according to its estimates.
“We are not in deflation,” Mario Draghi stressed.
He also warned that risks to economic growth across the 19 countries that use the euro remained “tilted to the downside”.
The ECB cut its growth forecasts to an increase of 1.4% in 2016 – down from 1.7%; 1.7% for 2017 – down from 1.9%; and 1.8% for 2018.
The governing council expected the bank’s key interest rates “to remain at present or lower levels for an extended period of time, and well past the horizon of our net asset purchases”.
The bond-buying program will continue at least until the end of March 2017.
As well as government debt, the ECB will now be allowed to use its newly printed money to buy bonds issued by companies as well. That scheme will start towards the end of the second quarter this year.
The euro initially fell 1% against the US dollar, but soon recovered to be trading higher and was also up against the yen. A weaker euro makes European exports cheaper, so the rise will not be welcomed by manufacturers.
European stock markets also rose sharply following the announcement before losing much of those gains, with Frankfurt up 0.6% and Paris rising 1%, although the FTSE 100 in London fell 0.2% and Wall Street was flat in morning trading.
Shares in European banks posted gains, with Deutsche Bank rising 4.8%, Societe Generale adding 2.7%, Santander up 5.5% and Italy’s UniCredit adding 6.8%.
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