The bill is considered an interim step on the path towards an eventual referendum for constitutional change.
Its passage through the Lower House was greeted with applause from the public gallery and coincides with the five year anniversary on which former prime minister Kevin Rudd apologised to the Stolen Generations.
Prime Minister Julia Gillard has described the legislation as a "sign of good faith" that Parliament is committed to righting the wrongs of previous actions.
"No gesture speaks more deeply to the healing of our nation's fabric than amending our nation's founding charter," she told Parliament.
"This bill seeks to foster momentum for a referendum for constitutional recognition of Aboriginal and Torres Strait Islander peoples."
The legislation passed with unanimous support.
Opposition Leader Tony Abbott says constitutional recognition for Indigenous people is long overdue.
"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," he told Parliament.
Mr Abbott has paid tribute to those who have worked to achieve reconciliation over a long period of time, including former prime ministers Gough Whitlam, Harold Holt, John Howard and Kevin Rudd.
He has also recognised the efforts of Ms Gillard.
"So often in this place, we are antagonists. Today on this matter, we are partners and collaborators," he said.
The preamble to the legislation notes that further consultation is necessary to refine plans for a referendum and to grow community support for the change.
"The Parliament is committed to building the national consensus needed for the recognition of Aboriginal and Torres Strait Islander peoples in our Constitution," the preamble states.
"The Parliament believes this Act is a significant step in the process towards achieving constitutional change."
Long-time Indigenous rights campaigner Patrick Dodson has welcomed the passage of the legislation, but says there is more work to be done to get full recognition.
"The passing of the Act of Recognition today is one hill we have climbed but it does not mean we have conquered the mountain," he said.
"We now need to work together put aside our differences and help each other to reach the top of the mountain."
He says the key task now will be clarifying the question for a referendum, something he says is on the shoulders of the nation's political leaders.
"It's not their own task and by no means is it exclusive to them, but it is ultimately at the end of the day what the politicians can agree and find accommodation with that we will vote upon."
Very few referendums have been successful because any change to the Constitution requires the support of a majority of people in a majority of states.
Ms Gillard has indicated that the referendum to recognise Aboriginal and Torres Strait Islanders in the Constitution is likely to be held next year.
Greens Senator Rachel Siewert says there now needs to be a full and frank discussion about the proposed wording to go into the constitution.
"We also need to make sure that we get the question right and that this referendum doesn't fail," Senator Siewert said.
"The Greens are totally committed to achieving this."
An expert panel set up to consider the options for constitutional change recommended amendments to recognise that Australia was first inhabited by Aboriginal and Torres Strait Islander people.
It also suggested there should be an acknowledgement of the need to "secure the advancement" of Indigenous people.
The panel recommended English be declared Australia's national language, but that Aboriginal and Torres Strait Islander languages be recognised as the country's first languages.