The data also showed that while most people live in a family situation, nearly 900,000 live together, while 2.5 million live alone.
The large majority of homes are detached, while 3.2 million dwellings have four bedrooms are more.
Launching the Census results on Tuesday, the nation's deputy statistician Teresa Dickinson said the number of homes owned either outright or with a mortgage hasn't changed significantly since 1996.
"However the share of homes which are owned with a mortgage, rather than outright, has been growing," she told a media conference in Canberra.
"Over the last 25 years the number of homes owned outright has increased by 10 per cent, while the number owned with a mortgage has doubled."
Of the 2.9 million homes that are owned outright, 2.4 million are standalone properties, while of the 3.3 million under a mortgage, 2.7 million are also detached houses.
There are 23.5 million Australians living in a private dwelling, 20.1 million of which are a family household.
A further 871,349 people live together as a group, while 2.5 million live alone.
Of the 6.2 million people who live in a home that is owned outright, 875,176 have a weekly income of $4000 or more, while of the 9.8 million paying off a mortgage, 2.4 million are in the same wage bracket.
There are seven million renters in Australia, of which 926,918 have a weekly salary of between $2000 and $2999 and 712,288 who have a weekly income of $4000 or more.
At the other end of the scale, there are 104,996 renters who have no income at all, the Census data shows.
There are 30,053 people who are purchasing a house under a shared equity scheme. The largest share of these, 2588 people, have a weekly salary of $650 to $799.