Treasurer Jim Chalmers announced on Sunday the new topics would be included in the next national snapshot to be held in 2026, following backlash from the LGBTIQ+ community.
The Australian Bureau of Statistics will write the questions.
Dr Chalmers said LGBTIQ+ Australians had been heard.
"We've had good intentions right throughout this, we want to do the right thing for the right reasons," he said.
"We've listened, we've taken that feedback seriously.Â
"We're going to get the right outcome here, which is really important, and we will continue to work with the community and with the ABS through the next stages of the process."
Previously, the government was of the view the proposed questions might be too complex and could spark a damaging culture war in the lead-up to the federal election, due by the end of May.
Equality Australia chief executive Anna Brown urged all politicians to back the proposal to get the changes through the federal parliament.
"This is the sensible, pragmatic and moral course of action, that will ensure vital data about some of the most vulnerable populations in Australia is collected nationally for the first time," she said.
Assistant Treasury Minister Andrew Leigh said the questions would be asked of people aged 16 and over and answering would be optional.
"The ABS did not recommend a topic on variations of sex characteristics (intersex status) in the census, and it will not be included," he added.
"We value every Australian, regardless of their faith, race, gender or LGBTIQ+ status."
The government plans to settle the changes before the end of the year.
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