Romania has jumped from being the 86th most common non-UK country of birth to the fourth in the space of 20 years.
Meanwhile, Jamaica and Kenya have tumbled out of the top 10, according to new analysis of the 2021 census data.
Other new entries in the top 10 include Poland and Nigeria, but there have been sharp drops for Australia and Canada.
The figures, released by the Office for National Statistics (ONS), show how the top non-UK countries of birth in England and Wales have changed in recent decades.
India was the most common non-UK country at both the 2021 and 2011 census, and the second most common in 2001.
Ireland has slipped from first place in 2001 to fourth in 2011 and fifth in 2021.
The rest of the top 10 has seen major changes, however.
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Romania ranked 86th in 2001 and by 2011 had climbed to 26, before jumping to fourth place in 2021.
Poland has risen from 18th in 2001 to second in 2021, while Nigeria is up from 14th to eighth.
But Jamaica has fallen out of top 10, dropping from sixth place in 2001 to 20th in 2021, along with the US (from seventh to 11th) and Kenya (ninth to 21st).
“The rise in position of both Poland and Romania is likely because they joined the EU in 2004 and 2007, respectively, and therefore gained entitlement to free movement,” the ONS said.
“These changes over the last 20 years reflect a notably different picture of international migration over time.”
This is borne out by trends further down the rankings, which show China rising from being 25th at the 2001 census to 12th in 2021.
Other notable movers were Spain (up from 23rd to 13th), Portugal (34th to 15th) and the Philippines (30th to 17th).
By contrast, leaving the top 20 are Australia, which has fallen from 11th place in 2001 to 26th in 2021, Cyprus (down from 15th to 37th) and Canada (17th to 38th).
The census takes place across the UK every 10 years and provides the most accurate estimate of all the people and households in the country.
The latest census was filled out by more than 24 million households across England and Wales on 21 March 2021.
