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.
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.
"It is too early to tell if this is an indication of a long-term trend."
The ONS figures show that immigration from all countries has fallen - and emigration has also risen.
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.