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Overall net migration, the difference between the number of people coming to live in the UK for at least 12 months and those leaving, was 270,000.
The government wants to cut overall net migration to below 100,000.
Some 226,000 EU citizens came to the UK and 138,000 EU citizens left in the year to the end of March.
"Much of the recent fall is in people from the western European countries that make up the 'EU15' group coming to the UK for a definite job," said ONS statistician Nicola Rogers.
Separate data from the Labour Force Survey for April to June 2018, shows there were 86,000 fewer EU nationals working in the UK than a year earlier.
That represents the largest annual fall since comparable records began in 1997.
ONS Migration Statistics Quarterly Report: August 2018