The National Institute for Economic and Social Research says 700,000 people moved to the UK after their former communist homelands joined the EU.
It believes they drove up British GDP by 0.38% in the years to 2009, the equivalent of £4.91bn.
The report says countries which imposed restrictions on eastern workers saw growth reduced because of this.
Only the UK, Ireland and Sweden allowed free access from the start to workers from the eight 2004 accession countries, which included Poland, Latvia and Hungary.
The last EU members to keep restrictions — Germany and Austria — lift them on Sunday.
Between 2004 and 2009, an estimated 1.5 million people from eastern Europe came to the UK. It is thought 700,000 of them stayed, with half a million from Poland alone.
During the same period Britain’s GDP grew by £98bn, or 7.7%, and the NIESR study says that a 5% share of the £98bn can be put down to the migrants.
The NIESR says the UK probably benefited from the restrictions imposed by other member states. It says Germany will suffer a “permanent scar” on its level of output, with its GDP reduced by between 0.1 and 0.5%.
One of the report’s authors, Dawn Holland, says that the final lifting of restrictions by all EU countries will make little difference to the situation.
“Lifting barriers in Germany may divert some Polish and other workers away from the UK”, she says, “especially given the relative strength of the German economy”.
“But as the existence of support networks for new migrants is one of the most important factors, much of the shift in migrants since 2004 is likely to prove permanent.”