The currency shake-up followed official euro zone data for the last three months of 2013, which showed the 18-country bloc's economy expanded 0.3 percent quarter-on-quarter. This was narrowly better than analysts' forecast of 0.2 percent growth, and topped the third quarter meager 0.1 percent expansion.
Investors were also pleased by the narrowing of growth between economic "strongman" Germany and struggling France, both of which still grew more than forecast. Germany grew by 0.4 percent while France expanded 0.3 percent.
"The euro area economy confirmed that a gradual recovery is under way, growing for a third consecutive quarter in the fourth quarter… Upside surprises in Germany, France and the Netherlands are the main drivers of today's higher-than-expected outcome," said Barclays analysts Apolline Menut and Fabrice Montagne in a research note.
Meanwhile, markets have struggled to interpret recent economic data out of the U.S., and what this might mean for the progress of Federal Reserve asset tapering under new Chair Janet Yellen.
On Friday, industrial production data for January showed a 0.3 percent decline, against expectations. However, the University of Michigan consumer sentiment reading came in stronger than expected at 81.2.
"The U.S. dollar remains on the defensive. One would never know looking at the price action in the capital markets that earlier this week, new Fed Chair Yellen made it clear that the tapering course that Bernanke put the Fed on at the end of last year will continue, barring a significant deviation from its expectations," said Brown Brothers Harriman currency analysts led by Marc Chandler in a note.
Bank of Tokyo-Mitsubishi's Derek Halpenny said the euro would struggle to advance beyond $1.3800, suggesting the European Central Bank (ECB) might feel forced to intervene given the region's worryingly low inflation levels.
He added that the strength of the euro against the dollar was symptomatic of both the fragility of the dollar and investor optimism on the euro.
"There really appears to be very little with the ability to undermine confidence in the euro," he said.
"An explicit hint that the ECB is 'very seriously' considering a negative deposit rate, the constitutional court decision in Germany on OMT (Outright Monetary Transactions)… and the collapse of the Letta government in Italy have all failed to register more than a momentary blip lower for the euro."
(Read more: Time to curb the enthusiasm about Europe?)
Meanwhile, U.K. sterling traded around a three-year high against the dollar on Friday, while the Japanese yen has gained about 3.2 percent against the greenback since the start of this year.
Halpenny said the dollar would likely continue to weaken against the euro should the U.S. continue to report indifferent economic data, and emerging markets remain steady.
"Mixed-to-weak data from the U.S. in circumstances of emerging markets remaining stable is the best mix for EUR/USD moving higher," he said.
—By CNBC's Katy Barnato. Follow her on Twitter: