People in the south Wales valleys were the most likely to describe themselves as Welsh, with Rhondda Cynon Taf having the highest Welsh-only identity.
Blaenau Gwent had the highest proportion of people born in Wales, while Powys had the lowest.
This was the first time a national identity question had been asked.
The 2001 census had proved controversial after it included a box for people to tick to describe themselves as Scottish or Irish but not Welsh.
If people wanted to class themselves as Welsh in 2001 they were told they could tick the box marked "other" and then write "Welsh" alongside.
The omission sparked protests and the Welsh government lobbied for a national identity question.
The Office for National Statistics confirmed in 2008 a Welsh tick box would be included in the 2011 census.
The figures have also been broken down by local authority, with 73% of Rhondda Cynon Taf's population (171,800 people) who said they saw themselves as Welsh only.
This was followed closely by Merthyr Tydfil, with a slightly smaller proportion, but was also 73% (43,100 people).
Merthyr also had the smallest proportion of people who described themselves as English (4%) or both English and British (less than 1%).
Statisticians said for every 20 people in Wales, 15 would be born in Wales, four born in England and one born somewhere else.
Only Cardiff has more than 10% of its population born outside Wales.
Almost two-thirds of people in Wales say they consider themselves Welsh, the 2011 census shows.