Prime Minister Julia Gillard has paid tribute to the courage her predecessor Kevin Rudd showed in apologising to the stolen generation five years ago.
Speaking to the Act of Recognition of indigenous people on the anniversary of the apology, Ms Gillard said the parliament was only able to consider constitutional change now because of Mr Rudd's action.
The recognition bill is intended as a precursor for a referendum to remove racist elements of the constitution.
Ms Gillard said while there was a decade of deliberation about the constitution, no indigenous people took part in its drafting.
"They had no opportunity to vote for it, and yet all were affected by what it said and what it failed to say," she told parliament on Wednesday.
The prime minister said the current push for change shared the idealism and dreams of the successful 1967 referendum which allowed indigenous people to vote and be counted in the census.
The Aboriginal and Torres Strait Islander Peoples Recognition Bill 2012 has a two-year sunset clause as a way of ensuring it doesn't replace constitutional change.
"The bill gives the parliament some of the tools it will need to build the necessary momentum for constitutional change," Ms Gillard said.
"I do believe the community is willing to embrace the justice of this campaign because Australians understand that indigenous culture and history are a source of pride for us all."
Opposition Leader Tony Abbott said Australia now had an opportunity to do what should have been done 200 or 100 years ago.
"We need to atone for the omissions and for the hardness of heart of our forebears to enable us all to embrace the future as a united people," Mr Abbott told parliament.
He said the example of New Zealand's Treaty of Waitangi showed how Australia could have done better.
But he hoped the Australian people's spirits would be lifted by parliament's actions.
"We shouldn't feel guilty about our past, but we should be determined to rise above that which now makes us embarrassed," he said.
Both leaders acknowledged finding a form of constitution that made everybody happy would be difficult, but not impossible.
"I believe that we are equal to this task of completing our constitution rather than changing it," Mr Abbott said.
Indigenous Affairs Minister Jenny Macklin gave the formal summing up of debate after Mr Abbott spoke.
"The Australian constitution is the foundation document for our laws and our government but it is silent on the special place of our first Australians," she told parliament.
"Today those of us here play our part in recognising this special place."
The bill passed the lower house unanimously to applause from full public galleries.
It now proceeds to the Senate.