Bulgarian and Romanian citizens are free to live and work in the UK after controls in place since 2007 expired.
Home Affairs Select Committee chairman Keith Vaz greeted the first flight from Romania as it landed at Luton airport on Wednesday morning.
Romanian Victor Spiersau was aboard and said: "I don't come to rob your country. I come to work and go home."
The UK has not released forecasts of migrant numbers, but campaigners say up to 50,000 people a year could come.
Immigration minister Mark Harper said curbs on access to benefits would ensure those heading to the UK would contribute to the economy. New arrivals
One of the plane's passengers, Victor Spiersau, was coming to the country for the first time.
Nigel Farage: "It's irresponsible to open the door unconditionally" The 30-year-old said he already had a car washing job lined up that would earn him 10 euros (£8) an hour - an improvement on the 10 euros a day he received working in the construction industry at home.
"I don't come to rob your country. I come to work and then go home," he said. "Here you pay a lot; in Romania it's very cheap."
Mr Spiersau added: "I don't want to stay here. I want to renovate my home and to make a good life in Romania because it's much easier to live in Romania because it's not expensive."
A Home Office spokesman said the government was working to reduce net migration and would ensure people entering Britain were doing so for the right reasons.
However, more than 60 MPs are backing a campaign to extend the restrictions for a further five years, saying the British economy has not sufficiently recovered from the 2008 recession to cope with the change and that it will put pressure on public services and reduce job opportunities for British workers.
Laszlo Andor, the EU commissioner for employment, social affairs and inclusion, said there were already three million people from Bulgaria and Romania living in other European Union member states.
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image of Mark Lowen
BBC News, Bucharest
It's a special new year for Romanians and Bulgarians, finally gaining equal rights to work freely across the EU seven years after their accession.
Some, particularly Britain, fear large numbers will come, mindful that a decade ago the government expected 15,000 per year from Eastern Europe but a million and a half came.
No extra flights have been planned from Bucharest but one coach company has tripled services to London.
Many here talk of their hopes of a better life with higher salaries - but nobody knows quite how many will finally leave.
"It is unlikely that there will be any major increase following the ending of the final restrictions on Bulgarian and Romanian workers," he said.
Mr Andor said his organisation recognised that migrant influxes could strain welfare systems in host countries but since the EU provided contingency funds for this it was no reason to put up barriers.
He said migrants were essential to economic recovery and must be protected from discrimination.
"I firmly believe that restricting the free movement of European workers is not the answer to high unemployment or a solution to the crisis," he added.
Migration Watch - which campaigns for tighter controls on immigration - has suggested that many of the two million Romanians and Bulgarians currently working in Spain and Italy could now be tempted to come to the UK by the higher wages and access to in-work benefits such as tax credits.
It says the UK remains the "most lucrative destination" for migrants across the EU, and estimates that 50,000 people from Romania and Bulgaria will move to the UK each year for five years.
"There's a definite possibility that some will start to shift in this direction," Migration Watch's co-founder, Sir Andrew Green, told BBC Radio 4's Today programme.
The Bulgarian ambassador, however, has previously estimated that...
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