However, progress is far from smooth and some countries, notably France, are lagging behind badly.
Some countries, it says, risk squandering their "hard-won gains" if they reverse some of their key reforms.
These are among the conclusions of a major study into Europe's economic health.
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The analysis was conducted by the Brussels based Lisbon Council, a think tank, and Berenberg, a leading international bank.
The 'Euro Plus Monitor' is an authoritative survey that measures the economic health of 21 European economies.
It ranks the economic performance of Eurozone countries, as well as Poland, Sweden and the UK.
Using a complex methodology, it ranks the best and worst performers.
It found that:
- Most countries continue to adjust to the challenges posed by the erstwhile euro crisis;
- The four countries that succumbed to the economic crisis first, Greece, Ireland, Portugal and Spain, reduced their adjustment efforts significantly in 2015;
- Some of the "erstwhile laggards are now shaping up," including Italy, thanks to its pro-growth reforms;
- France has "finally" started to address some of its serious structural problems and
- While still in good fundamental health for the time being, Germany, the Netherlands and Sweden are showing "even more signs" of complacency.
Speaking at the launch, Valdis Dombrovskis, European euro and social dialogue Commissioner, said the report underlines the importance of the EU's economic reform process; "We fully acknowledge that the reform strategy requires political courage to tackle powerful vested interests. Some reforms may bear budgetary costs and others may be technically complex.
"Very often countries also face challenges in terms of their administrative and institutional capacity. Mere legislation is not enough. Effective implementation is what counts."
The report, published on Monday, says that while the Eurozone's initial economic recovery was driven mostly by exports, consumer spending has now taken over as the major contributor to demand growth.
"As a result, the recovery is more broad-based and better entrenched than before," it states.
However, "potential political shocks" such as a Brexit or reform reversals are now the "major potent risks to watch."
The score for the UK (No. 12, down from No. 10) dropped to 3.5 (down from 4.0 in 2014), the second significant slippage for Britain in a row.
There were two major reasons for the lower score.
"First, in election year 2015, the UK slowed the pace of structural reforms. Second, labour costs rose by 0.4 per cent in 2015 whereas they fell by 0.6 per cent in the Eurozone."
The mediocre ranking for Germany (No. 12) needs to be seen in context, says the report.
"Although Germany has gone through hardly any austerity since 2009, its sustainability gap remains so small that, unlike France, the shortfall is no reason for concern for the time being."
It adds, "As it continues to benefit from the rapid rise in employment and tax receipts unleashed by its 2004 labour market reforms, Germany has the fiscal space for the extra spending on refugees."
Germany, along with Sweden and the Netherlands, need to "stop their slippage and implement more serious pro-growth structural reforms."
"Otherwise," the report cautions, "they will lose their competitive edge over time."
The report says the "real problem" in the Eurozone remains France (No. 17), adding, "The inflexible French labour market has still not responded adequately to the challenge of high unemployment."
"Labour costs remain excessive but France is at least taking some steps in the right direction," it adds.