"Older people thought they would never live to see this day," King said. "It's very emotional for me and it's very important."
The "stolen generation" were the victims of policies that separated mostly mixed-blood Aboriginal children from their families.
From 1910 until the 1970s, about 100,000 Aboriginal children were taken from their parents under state and federal laws based on a premise that Aborigines were a doomed race and saving the children was a humane alternative.
A national inquiry into stolen generation held in 1997 found that many children taken from their families suffered long-term psychological effects stemming from the loss of family and culture.
The apology, an issue that has divided Australians for years, is to be the first order of business for parliament as it resumes for the first time since the November elections that put Rudd in power.
Rudd has said he is determined to raise living standards for Aboriginal Australians, many of whom live in remote, impoverished camps.
Michael Mansell, legal director of the Tasmanian Aboriginal Centre, has urged the government to set up a one billion Australian dollar ($882 million) compensation fund.
The 1997 inquiry into the stolen generation also recommended the payment of reparations.
But the Rudd government has refused demands to pay compensation.
Australia's previous government refused to offer an apology to Aborigines for past wrongs and implied that saying sorry would place the blame on the public.
Brendan Nelson, the opposition leader, whose conservative Liberal Party was thrown out of office in November after almost 12 years in power, questioned whether the apology deserved to be the new government's first item of business.