The number of foreign-born residents in England and Wales has risen by nearly three million since 2001 to 7.5 million people, the 2011 census shows.
That means about one in eight - 13% - of residents were born outside the UK.
The most common birthplaces outside the UK for residents are India, Poland and Pakistan. The number of ethnic white British people is down to 80%.
London has become the first region where white British people have become a minority.
Some 45% (3.7 million) of people in the capital described themselves as white British, down from 58% (4.3 million) in 2001.
The Office for National Statistics said the findings showed a "diverse" and "changing" picture.
More than half the rise in the population of England and Wales was due to migration.
Alp Mehmet, from Migration Watch, said the figures showed "how absolutely essential it is that we bring immigration under control".
He told BBC Radio 4's World at One that society must consider "the housing that's going to be needed, the schools that are going to be needed, the roads".
If people wanted "new arrivals" to be integrated, "then for goodness sake we can't have them arriving at this sort of scale", he added.
But Sunder Katwala, director of British Future - an independent think tank on migration - said people had "an absolute moral responsibility to make our society work as a shared society".
"The question of do you want this to happen or don't you want this to happen implies that you've got a choice and you could say 'let's not have any diversity'," he told the BBC News website.
"This is who we are - it's inevitable."
Guy Goodwin, from the Office of National Statistics, told BBC News: "It's a really changing picture so the 2011 census population will go down as a diverse population compared with 2001."
In other findings:
- The number of people living in England and Wales is up 7% to 56.1 million
- The Christian population was down 13 percentage points at 59% (33.2 million) in 2011, from 72% (37.3 million) in 2001
- The number of those who said they had no religious affiliation increased by 10 percentage points from 15% (7.7 million) in 2001 to 25% (14.1 million) in 2011
- 4.8 million people hold a foreign passport: 2.3 million from the EU and 2.4 million from outside the EU
- Norwich was the place with the highest proportion of people reporting
- London had both the largest proportion of residents born outside the UK (37%) and non-UK nationals (24%)
- 2 million households with at least two people had members from different ethnic groups in 2011, a 3% increase on 2001 (1.4 million)
- The employment rate is estimated at 71.8%; unemployment is 7.5%
- In Northern Ireland, the number of Protestants is now 48% (down 5 percentage points on the last census) and Catholics 45% (an increase of 1 percentage point)
- Again in Northern Ireland, two-fifths (40%) saw themselves as British only, while a quarter (25%) identified themselves as Irish only and just over a fifth (21%) saw themselves as Northern Irish only
- The number of people who speak Welsh has fallen in the past 10 years
The census also shows that, while fewer people own their own home, more people own it outright.
Just under 15 million households owned their own home in 2011, either with a mortgage or loan, or outright - down 4%.
However, those who owned their home outright increased two percentage points from 29% (6.4 million) to 31% (7.2 million).
The group that rented from a private landlord or letting agency increased by six percentage points from 9% (1.9 million) in 2001 to 15% (3.6 million) in 2011.
Campbell Robb, chief executive of housing charity Shelter, said the figures "confirm that home ownership is slipping further and further out of reach, no matter how hard people work or save".
Last year there was an average of 12 cars for every 10 households - up on 11 cars per 10 households in 2001. London was the only region where the number of vehicles was lower than the number of households.
The 2011 Census results for Scotland are drawn up separately by the Scottish government and are being released on Monday.
This year's questionnaire was sent to about 26 million households in England and Wales on 27 March last year and was compulsory to fill in.
The only voluntary question in the census related to religion and allowed people to declare themselves to be Christian (all denominations), Buddhist, Hindu, Jewish, Muslim, Sikh, of no religion or to list themselves as belonging to any other faith.
The census - which is used to plan public services - is carried out every 10 years, during which the public are asked questions about their jobs, health, education and ethnic background
Last year was the first time people could fill in the form online.