Net migration has fallen to the lowest level for three years after a surge in the number of EU nationals leaving the UK since last June's Brexit vote.
Net migration - the difference between those entering and leaving the UK - fell 81,000 to 246,000 in the year to March 2017.
More than half that change is due to a decrease in net migration of EU citizens, which is down 51,000.
The government is committed to reducing net migration to below 100,000.
Non-EU students 'not staying illegally'
Immigration Minister Brandon Lewis welcomed the new figures, saying: "It was good to see a third quarter running of net migration figures coming down".
But business groups raised concerns about the fall, with the CBI saying: "The loss of these vital skills should concern us all."
The ONS figures show a particularly sharp rise, of 17,000, in departures of citizens from the so-called EU8 countries - Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia and Slovenia.
An ONS spokesman said: "These results indicate that the EU referendum result may be influencing people's decision to migrate into and out of the UK, particularly EU and EU8 citizens.
International migration for work remains the most likely reason to move, said the ONS, but it added that people are now more likely to move if they have a definite job, rather than to just look for work.
A spokesman for the Institute of Directors said "no one should celebrate these numbers".
"Given unemployment is currently at its lowest level ever (4.5%), without the three million EU citizens living here the UK would have an acute labour shortage.
"Signs that it is becoming a less attractive place to live and work are a concern," he added.
Are there other factors beyond a suspected Brexit effect?
Since the Brexit referendum, the falls in the pound on currency markets mean that money made in the UK buys less back home.
This is really important for workers who are sending cash back to their families - and a decisive factor in decisions to move all around the world.
Last June, the pound bought almost 6 Polish zlotys. Today, it buys only 4.6 zlotys.
What's more, when people choose to move to another country, they're not just looking at the circumstances there, but, fairly obviously, at the conditions at home.
And there is no doubt that for some EU workers, coming to the UK isn't the slam-dunk deal it once was.
Matthew Percival, head of employment at the CBI, said EU nationals made a "crucial contribution" to the economy.
"This latest data reflects a trend many businesses have seen - an increase in the number of EU citizens leaving the country," he said.
"The loss of these vital skills should concern us all, underlining the importance of urgently providing certainty for millions of workers and their families."
The government has also published the first ever "exit checks" data - a proper count of all people who are actually known to have left the UK.
For the year to March 2017, the data shows that 97% of students from outside the EU with a visa to enter the UK are known to have complied with the terms of their visa by either departing the UK or remaining in the country by extending their visas.
It is not clear what had happened to the remaining 3% whose visas had expired.
This previously unknown figure runs contrary to repeated claims that international students are abusing the immigration system to stay illegally in the UK.
Labour's shadow home secretary Diane Abbott said it showed Theresa May's "long-running campaign to malign international students" was "based on fantasy".
And Labour leader Jeremy Corbyn said the NHS was facing recruitment problems due to the lack of EU workers - and the UK needed a migration policy based on the "economic needs" of the country.
The Lib Dems called the overall drop in net migration a "deeply worrying Brexodus of EU citizens", blaming the government's failure to guarantee their rights to stay in the UK after Brexit.
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