The OECD's annual migration outlook said numbers of migrants from countries most affected by the crisis -- particularly those in southern Europe where eurozone debt is worst -- had risen 45 per cent from 2009 to 2011.
The number of Greeks and Spaniards to have migrated to other European Union nations since 2007 has doubled to 39,000 and 72,000 respectively, it said.
The number of Greek migrants to Germany increased 73 per cent between 2011 and 2012 while the number of Spaniards and Portuguese was up almost 50 per cent, with Italian migrants increasing 35 per cent.
In what it called the first international study of the impact of migration on public spending in a time of high unemployment and debt, the OECD said the overall effect of immigrants on host nations was close to zero.
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But unemployment among migrants is a growing problem.
Almost one out of two unemployed migrants had been looking for a job for over a year in 2012, the report said. The rate of joblessness among foreign-born people rose five percentage points between 2008 and 2012, compared with three points for the native born.
But the report downplayed the impact of migrants on the economy.
"Overall, it shows that the fiscal impact of immigration is close to zero on average over the OECD," it said.
"If the results described above tell us anything, they tell us that more immigration does not necessarily mean more public debt."
The Paris-based OECD is a forum for policymaking and analysis grouping 34 advanced economies.