"In Italy and France, the signs of a positive change in momentum, which were assessed as tentative in March, have now been confirmed," the OECD said in a statement.
The OECD's composite leading indicators (CLIs), designed to anticipate turning points in economic activity, also showed a positive change in momentum for Germany.
The figures will come as a relief to the European Central Bank, which recently launched a €1.1 trillion ($1.2-trillion) bond buying programme to boost sluggish growth and ward off deflation.
Of particular concern have been France and Italy, the eurozone's second and third-largest economies, which have been stagnating.
In Italy, which saw its economy contract 0.3 percent last year, the government is forecasting 0.7 percent growth this year.
France's government is forecasting 1.0 percent growth this year, after a meagre 0.4 percent expansion in 2014.
The Paris-based organization, which provides economic analysis and advice to its 34 industrialised country
members, said the growth outlook was stable in the OECD area as a whole as well as for the United States, Britain and Japan.
Meanwhile, "CLIs signal growth easing in China and Canada, albeit from relatively high levels."
China, not an OECD member, has been a major source of global growth, but the world's second-largest economy has been experiencing a broad slowdown in recent years.
Purchasing manager surveys, one leading indicator, have recently shown Chinese manufacturing steady, while official data released earlier this month showed output, retail and investment growth have all fallen to multi-year lows.
China's economy expanded 7.4 percent last year, the worst result since 1990, and earlier this month leaders lowered this year's target to approximately seven percent.
For other emerging markets, the CLIs point to slowing growth momentum in Brazil and Russia, and firming growth in India.