The euro initially fell 1.6% against the US dollar to $1.0822 before jumping as high as $1.1218.
It was one of the biggest one-day swings in the currency's history.
Sharp rises for European banks were also largely wiped outThe ECB cut its main interest rate from 0.05% to 0% and cut its bank deposit rate, from minus 0.3% to minus 0.4%.
The bank will also expand its quantitative easing programme from €60bn to €80bn a month.
Jasper Lawler, of CMC Markets, said: "Stocks came off highs of the day when some of the initial euphoria was nullified by the suggestion by ECB president Mario Draghi that rates would not be cut any further."
Simon Derrick, chief currency strategist at BNY Mellon: "If the intention of the ECB board was to help weaken the euro then their work was entirely undone by Mr Draghi's comments about the future path of rates."
John Hardy, head of currency strategy at Saxo Bank, said: "This was a much bigger bazooka than the market was expecting and shows the ECB trying to get ahead of the confidence curve after learning its lesson in December."
The stimulus measures announced three months ago have largely failed to drive economic growth higher or boost inflation.
Read more: ECB stimulus surprise sends stock markets sliding - BBC News