Fears of a "flood" of Eastern Europeans coming to the UK after EU enlargement have not materialised, says Des Browne.
Mr Browne's speech was organised by the Institute for Public Policy Research
Europe expanded from 15 to 25 states on 1 May with eight of the new members being ex-Communist states such as Hungary, Poland and Lithuania.
But the immigration minister said that most workers registering since 1 May were already in Britain.
"Early indications are that there has not been a 'flood' of new entrants," he said in a speech to think tank IPPR.
Government estimates originally suggested that around 13,000 people would arrive from the new member states each year.
Some groups were claiming that the number would be far higher and there were newspaper reports that Britain would be "flooded" with Eastern Europeans looking for work.
"Information on the effects of accession - including the numbers applying to register under the worker registration scheme - will be published in due
course," said Mr Browne in a speech at the Slovak embassy in west London.
Benefits to Britain?
He added: "The rights of nationals of the enlarged EU to travel freely, take up residence in any member state, study, and in the UK, to engage in economic activity, are to be celebrated.
"Allowing new EU citizens to access the UK's labour market under the workers registration scheme makes good economic sense.
"The UK is benefiting from increased labour market flexibility and a pool of workers with the skills, qualifications and willingness to help fill skills
shortages in sectors like hospitality, catering and agriculture."
He said another benefit was that formerly illegal workers from these countries could no longer undercut genuine employers.
Current trends suggested most of the people coming to Britain looking for work would do so for "limited periods of time - weeks or months, rather than years".
The government's decision to introduce work restrictions affecting citizens from Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia and
Slovenia caused a political row.
Britain had been the last of two existing EU states, including Ireland, not to introduce the limits but then the government changed its mind.
At the time Tory home affairs spokesman David Davis was highly critical of ministers whom he said had got themselves in a "mess" over the issue.
Malta and Cyprus - the other two new members - were exempt from the employment rules.