The terms Asian Welsh and Black Welsh will be included in the 2021 census.
It follows criticism last year over a draft of the questionnaire.
It offered respondents an option to identify as White Welsh as their ethnic group, but did not offer similar recognition for people who consider themselves Asian Welsh or Black Welsh.
The questions were changed following talks between the Welsh Government and the Office for National Statistics.
In the draft questions on ethnicity, the census planned to have a tick-box for people to identify as White "Welsh, English, Scottish, Northern Irish" or "British".
A separate question on nationality does allow respondents to identify as Welsh, but tick-boxes for people to identify as Asian or Black as their ethnicity did not include a Welsh option.
Under the changes, the headings for the options for people from Asian and black backgrounds, will include the terms "Asian Welsh" and "Black Welsh", as well as Asian British and Black British.
BBC Wales understands the intention is to make the language more inclusive.
The tick-boxes themselves - which attempt to identify an individual's ethnic background - are not expected to change.
If someone wants to register Welsh as their background and they are not white, it will need to be written in.
The Office for National Statistics (ONS) was asked by the Welsh Government to review the wording of the questionnaire "to make it as inclusive as possible for the non-White Welsh population".
"Following this review, including the testing of options and taking account of other evidence and research, the ONS has recommended that the questionnaire in Wales includes the terms 'Asian Welsh' and 'Black Welsh' in the high-level descriptions, alongside 'Asian British' and 'Black British' in the ethnic group question," the ONS added.
A Welsh Government spokeswoman said the change "will be reflected in the 2021 Census questionnaire in Wales".