But the recovery is filled with worries, so much so that the European Central Bank is poised to deliver stimulus measures that are more usual for economies mired in recession rather than those on the upswing.
Figures on Thursday are expected to show that the economy of the 18 countries that use the euro expanded by 0.4 percent in the first quarter from the previous three-month period. That's double the rate recorded in the previous quarter and would mark the third straight quarterly expansion.
The recovery is clearly a source of hope for a region that's spent most of its time since 2008 in the midst of crisis. The global financial crisis, which threatened the banking system, exposed the weak underbelly of the whole euro project - the shaky state of the public finances of many of the currency's users, including Greece, Portugal and Italy.
Growth, even if shaky or uneven, is key to moving past those troubles.
Positive signs of late include:
Five straight months of modest declines in the number of unemployed people. A year ago there were fears that unemployment in the eurozone would breach the 20 million mark. It's now fallen to around 18.9 million and the rate has declined to 11.8 percent from the record 12 percent.
Surveys of purchasing managers have pointed to a pick-up in sentiment among business executives at levels indicating solid expansion.
Buoyant growth in Germany, Europe's biggest economy. The country and its high-value exporters have benefited hugely from the rebound in world trade.
Glimpses of recovery in those countries hardest hit by troubles over too much debt. Spain, which needed a 41 billion-euro ($56 billion) bailout loan from other eurozone countries to rescue its banking system, has already reported growth of 0.4 percent for the quarter, its highest in around six years. And Greece's output may have halted its plunge, though its economy is some 25 percent smaller than its peak in 2008.
Yet, amid all that, European Central Bank head Mario Draghi all but promised more stimulus measures when the bank's rate-setting council next meets on June 5. Draghi said last Thursday that the council was "comfortable with acting next time."
Measures could include an interest rate cut, as well as unconventional steps such as charging banks a negative interest rate for money deposited with the central bank - in the hope they opt to lend to businesses and consumers instead.
These sort of measures are more common when central banks are dealing with a deep recession or crisis such as the one following the collapse of U.S. investment bank Lehman Brothers in 2008 - not during a rebound.
Here's why the eurozone recovery may need more help:
Inflation is dangerously low at an annual rate of only 0.7 percent. That's well below the ECB's goal of just under 2 percent. Low inflation makes it harder for countries to pay down excessive debt levels they have built up. There's still a risk the eurozone might fall into outright deflation, a downward price spiral that has the potential to choke off growth if consumers delay spending in the hope of bargains further down the line or businesses grow reluctant to invest or innovate.
"The reason why the ECB is still thinking about stimulus is that deflation could push the eurozone back into the kind of crisis we had a couple of years ago," said Tom Rogers, senior adviser to the EY eurozone economic forecast. "The ECB is trying to provide a little extra momentum to get the eurozone up to what you might describe as escape velocity."
Unemployment, while falling slightly, is still painfully high, particularly in those countries most afflicted by the debt crisis - 25.3 percent in Spain and 26.7 percent in Greece. Sky-high unemployment gives workers little bargaining power for higher wages. Flat wages contribute to low inflation and mean less spending on the goods made by businesses.
A strong euro is also threatening to hold back exports by making them more expensive in overseas markets. Draghi's comments last week helped contain the damage, sending the euro down from a near 2- 1/2 year high around $1.40 to around $1.37. The prospect of lower interest rates can weigh on the value of the currency.
The ECB might go farther, and use newly created money to purchase corporate or government bonds on financial markets. That pushes money into the hands of banks, in hopes it will be loaned to companies or invested in ways that expand the supply of money in the economy. Expanding the money supply could help increase inflation.