The final Markit Eurozone Composite Purchasing Managers' Index (PMI) for February was 53.3.
This was higher than an earlier, preliminary estimate of 52.7, and above the 50 level that indicates expansion.
Markit said the figures indicated the eurozone is set to grow by 0.4-0.5% in the first quarter of 2014, which would be the best growth for three years.
Official figures, also released on Wednesday, confirmed that the eurozone grew by 0.3% in the final three months of 2013. Growth was helped by rising exports and improving investment.
The PMI survey confirmed the contrasting fortunes of Germany and France.
German companies saw strong growth, with the country's composite PMI reading hitting a 33-month high of 56.4.
However, activity among French firms continued to decline, with the PMI figure dropping to 47.9.
The European Central Bank (ECB) holds its latest meeting on Thursday, and there has been speculation that the bank may take action to avert the threat of deflation in the eurozone.
Eurozone inflation was 0.8% in February, well below the ECB's target of 2%.
Business growth in the eurozone accelerated last month to its fastest pace since June 2011, a survey says.